They did in fact give a flat "no" to both George and Ukraine, and that was the key outcome of the 2008 Bucharest Summit. What you seem to be missing here is that despite the nice-sounding press release you shared in the other comment, their formal application, in the form of their requests for what's known as a Membership Application Plan, was denied:

   From 2008, Russia began stating its opposition to Ukraine's membership. That March, Ukraine applied for a Membership Action Plan (MAP), the first step in joining NATO. At the April 2008 Bucharest summit, NATO Secretary General Jaap de Hoop Scheffer declared that Ukraine and Georgia would someday join NATO, but neither would begin Membership Action Plans.

One can read those various press releases ("communiqués") that came later as hedges / equivocations -- but that's all secondary. At the time, it was crystal clear that their applications had been rejected, and this was really quite a bit deal at the time.

As to whether we would be in the current situation right now: that gets into hypotheticals of course, but the main point is that Putin definitely did not launch those invasions simply "because NATO", but because his disappointment with the change of government in Kyiv in 2014 (and at least one of Putin's insiders has said there had been plans to at least re-take the Crimea since way back in the early 2000s).

That's why the whole NATO encroachment line is basically a foil -- it's just something Putin says, but it's not the reason he launched those invasions.