It doesn't seem in dispute that Russia has breached the Budapest Memorandum
Russia probably disputes this or considers the memorandum invalid, so the statement is not quite correct. But I assume that everyone understands what is meant here - Ukraine and its allies do not trust Russia to hold its promises.
Trust in everyday life
Trust in politics does not mean the same thing as trust in everyday human life. In the everyday life trust is essentially a belief that another person will behave in a certain way due to their emotional connection to us, or their moral principles, or simply due to their character (aka "You can't trust Melanie, but you can trust Melanie to be Melanie.") Thus, the trust depends on us knowing the characteristics and attitudes of the other person, i.e., their past behavior. If they broke our trust, we do not trust them again, or trust them less, or demand that they regain our trust by showing good behavior.
Trust in politics
In politics, when dealing with state actors, there are no friends or enemies, but only interests. So trust is based on understanding the interests of the other side, how far they are prepared to go in the name of defending their interests, and what they may consider as a threat to these interests. In some cases, of course the interests of a state actor are closely related to those of one or several people at the top - however, even in dictatorships and kingdoms the people at the top are usually not free to do whatever they want (or may lose control, if they try).
One can rarely have full understanding of what really matters for the other side, what it is prepared to do in the name of protecting its interests, and how easily it can muster the necessary means. This is why one relies on small clues dropped by the other side. Exchanging such clues is referred to as confidence-building measures, and some of the more evident ones can be encoded in international agreements, peace treaties, etc.
Example: Demilitarized zone
Creating a demilitarized zone is a good way to convey non-agressive intentions to the other side. E.g., under Egypt-Israeli peace treaty Israel had returned to Egypt the Sinai peninsula, captured in a previous war. One of the conditions of the treaty stipulated that the Sinai would be demilitarized - that is limited the amount of the Egyptian forces present in the peninsula. (Demilitarization is sometimes taken literally these days, as no military at all - this is not quite the case in practice.) This way Israel could be sure that Egypt could not mount a sudden military attack or, if it did try to launch an attack, Israel would have time to detect the troops movements and prepare accordingly. When, in the wake of the Arab spring, Egypt needed to transfer additional military forces to Sinai, in order to counter disorders, it clearly communicated to Israel these intentions and the amount of the forces it needed, so that Israel would not treat it as an act of aggression and could take proportional counter-measures.
Finland and Sweden famously didn't enter NATO, as a means of keeping their independence and following pro-western political and economic development, without provoking the USSR. The basis for this arrangement was that: on the one hand, USSR couldn't tolerate NATO presence on its border, within a few dozen kilometers from Saint-Petersbourg (then Leningrad). On the other hand, the Winter war has shown that overrunning and occupying Finland could be very costly to the USSR. So the Soviet cost-benefit balance was to leave Finland to its own devices, unless it tries to enter NATO - in which case it would probably have to be attacked, whatever the costs are. There was likely much of diplomacy involved to make clear to everyone where the red line passed for the USSR.
As nowadays Finland and Sweden ponder whether to enter NATO, it is again a matter of similar cost-benefit analysis: whether it is better to seek/have NATO protection, knowing that Russia is ready to counter it by military force at the first opportunity, or whether it is better not to provoke Russia and trust that it is too costly for Russia to fight on this flank. Of course, Russian interests are not the only factor that matters here - public opinion and anti-Russian sentiments could easily tip the scale for the government deciding one way or the other.
Similarly, in the Ukraine-Russia negotiations the trust will be based on whatever guarantees they can provide to each other, rather than just Putin's or Zelensky's word. E.g., concluding a separate security treaty, including the US, Russia and other neighboring countries, as Ukraine now proposes, could be such a measure: on the one hand, it would allow Ukraine to buy American weapons and host some American troops, which would guarantee its security from a new Russian attack. On the other hand, this US presence would be limited in comparison to that in NATO members, and, even if attack does take place, it would not be considered an attack against NATO with all the consequences. This way Russia might find more beneficial to leave Ukraine rest in peace, while Ukraine would know that Russia has more to lose by attacking it than by maintaining the status quo.
Russian lannguage version of the Wikipedia article on the Budapest memorandum points out that Ukraine and Russia have divergent interpretations of the memorandum and Russia does not consider to have violated it. The passage contains references to the official statements and documents in Russian, but, since these are official government documents, they probably can be found in translation. The following is Google-translated:
Russia officially denies accusations of violating the Budapest Memorandum and its applicability to the situation of “domestic political origin” in Crimea, since Russia, when drafting the memorandum, “did not undertake to force part of Ukraine to remain in its composition against the will of the local population”, as well as accuses the United States and the EU of violating the memorandum (which supported the opposition during the Euromaidan and, in particular, threatened to impose sanctions against the Ukrainian authorities), and accuses Ukraine of “long-term violation of obligations to counter the growth of aggressive nationalism and chauvinism”, respect the rights of national minorities provided for in the joint statement of 1994. According to Russia, the common element of the Budapest Memorandum and the concept of "negative assurances" is only the obligation not to use or threaten to use nuclear weapons against non-nuclear states, and this obligation of Russia to Ukraine "has not been violated in any way", and other paragraphs of the document only "duplicate provisions of the Helsinki Accords" and "have nothing to do with the non-proliferation of nuclear weapons". Referring to the absence of large-scale hostilities in Crimea at the time of its annexation, Russia also rejects accusations of violating the general ban on the use of force or the threat of force against Ukraine.
Remark: From my personal experience, it is not uncommon that the matching Wikipedia entries in different languages are not exact translations of each other, but rather written by different people, and often contain complimentary information.