From the article NATO Expansion: What Gorbachev Heard that is also cited in another answer looks like M.Gorbachev have heard some phrases that might be interpreted as having an option to agree on not expanding NATO, but were not such promises by itself. These are the phrases like:
- NATO should rule out an ‘expansion of its territory towards the east, i.e. moving it closer to the Soviet borders.’
- The Russians must have some assurance that if, for example, the Polish Government left the Warsaw Pact one day, they would not join NATO the next.
- well it is important to have guarantees
- We must find ways to give the Soviet Union confidence that its security would be assured
- Certainly any extension of the zone of NATO would be unacceptable.’
- NATO expansion is unacceptable (not a promise, still)
- would you prefer a unified Germany to be tied to NATO, with assurances that NATO’s jurisdiction would not shift one inch eastward from its present position?
and, from the screenshot of another answer:
- We had made it clear during the 2+4 negotiations that we would not extend NATO beyond the Elbe
Here there is more to say. In 1991 Germany signed the agreement not to allow foreign military bases and nuclear weapons into the former Eastern Germany. This agreement is followed but it does not apply to Nato expansion outside this territory, and does not disallow dislocation of the own German military forces there or also further into the East. There is a known fake that it does, going as far as Germany would not be allowed to have the own army at all, but the agreement only
restricts the size of the army that is currently well below that limit. Looks like some additional agreement with more restrictions have been discussed but even the originators of the fake admit, not signed.
These English constructs do not mean that the promise is being given. They say that something needs to happen or would happen under some circumstances that may or may not come true. They do not say this "something" has happened already in the past.
It should have been at least professional English translators, leave alone lawyers on the Russian side to understand that no promise is being given with such a sentences. They should have asked for the clearly worded and signed document. If such was refused, the should have thought about, why. Hence I am sure Russia has been fully aware they have no promise. Selling the used bicycle can be solved with handshake but not the fate of multiple nations, consisting of millions of people.
This also does not need to be not a honest behavior. It may be that the requirement to for an agreement not to extend NATO has been dropped because of Russia receiving something else in exchange like multi billion gas purchases, for instance, or elimination of some nuclear weapons on American side. It may be many items on the table of the negotiations, some just return back to the portfolio where they were pulled from without making into signed agreements.