Those people are wrong.
Why did countries of Eastern Europe want to join NATO? It was because they were concerned about the threat from Russia, a concern that has proven justified. So Russia is responsible.
I can see your point. Poland, Hungary and the Czech Republic joined not long after the two wars in Chechnya. However, Chechnya was already part of the Russian Federation. Arguably, it had the right to independence, since it had in 1917 gained independence for a bit before being forced to join the Soviet Union, and prior to that it had had ongoing conflict as it tried to resist Russia. Since Poland, Hungary and the Czech Republic do not share a border with Russia, I'm not sure that there was a huge threat to them at the time. So I don't quite buy that the Chechnya conflict was evidence of a great threat to Eastern European countries.
But even if it had been, membership of NATO requires no pre-existing conflicts at the time of joining, and a pre-existing threat seems like a similar, albeit less severe, reason not to allow membership, as it means an increased risk of bringing NATO into conflict. It treats NATO as an insurance policy for high risk countries.
This is nonsense. Germany was kept in check bu being a member of the EU. NATO continued because the threat from Russia had not gone away.
I got the idea from
"Why the Ukraine Crisis Is the West’s Fault" which says, "As the Cold War came to a close, Soviet leaders preferred that U.S. forces remain in Europe and NATO stay intact, an arrangement they thought would keep a reunified Germany pacified. But they and their Russian successors did not want NATO to grow any larger and assumed that Western diplomats understood their concerns."
What was the evidence for the continued threat from Russia in 1991?
That didn't work out for Ukraine.
I still have to read up on Ukraine's attempt to remain neutral prior to 2014.