The 2nd question in the poll maybe telling. Until 2012 only 2%-3% of respondents considered Russia the biggest threat. The perception of the threat increased with the invasion of Crimea. The belief that Russia has influenced the US election in 2016 doesn't seem to effect the opinion much. The number of people who consider Russia to be the biggest threat in 2018 is 19% -- only 4% higher than the number of people who considered Russia to be the biggest threat in 2015.
It maybe helpful to note that last week was the week that Lisa Page and Peter Stzrock testified before the House about the allegation that they conspired to taint investigations which influenced the last Presidential election.
So the complete picture of what was happening when President Trump made his statement can be summed up with the following facts:
- Trump and a number of people on the right stated that they considered China to be the biggest international threat to the US.
- Trump established a good working relationship with the President of China despite this threat.
- There are a number of yet-to-be-resolved scandals surrounding investigations (and alleged influence) of 2016 elections by US law enforcement and intelligence agencies. Some allegations indicate undue influence against the Trump campaign.
- Trump was in the process of attempting to normalize a heated relationship with the Russian Federation.
- A number of Russian Federation citizens were formally indicted in the US for actual crimes (e.g., hacking into electronic systems). Russia did not deny that these citizens committed those crimes although it did disavow any sanctioning of these activities.
- The opposition party is attempting to downplay the scandals surrounding law enforcement's role in 2016 elections to score political points against a sitting President.
All of these facts taken in concert provide a fairly good incentive for President Trump to act the way he does.
Given that the claims made by BBC were made about public statements, these claims can be evaluated as to their merit. They are, at best, exaggerations. President Trump stated that Putin emphatically denied sanctioning the hacking. What was unambiguously missing from Trump's statement was any (even the slightest) hint that he believed Putin.
Trump was in the process of attempting to create a better relationship with another country (his job). While personal insults had worked with other national leaders, President Trump clearly thought that this approach was not the best course of action in this instance.