It's really not just the Kremlin questioning the wisdom of NATO expansion - advisors within the USA policy apparatus have done the same, there have often been op ed pieces in the mainstream press - not now the country is so embroiled in Ukraine, but certainly in the past.
As for the assurances to Russia - well, that's the million dollar question isn't it. At the time of the initial assurances the soviet union hadn't collapsed and Ukraine wasn't independent. They occured in the context of the reunification of Germany, which was issue enough for the Soviets.
However there is record of assurance continuing to the time of the Minsk Agreement - was that intended to be wider? Also, Bush himself seemed to think there was a long term aspect to the assurances that he started, in internal communications and never to the Soviets, dialling back from. For some, all of that is irrelevant as the USA shouldn't be held to an old promise which events have overtaken. For others, the key reason events have overtaken the original entente is due to broken promises.
Anyway it has been a point of contention between NATO and Russia for decades and it's doubtful it's going to be ironed out by posters on Mumsnet, sadly.