The point was correct but poorly stated. It's not the problem of NATO at its border. It's the problem of NATO at the border with Ukraine specifically. That is the border Russia has been invaded over 3 times. Napoleon invaded Russia through that border and that's considered one of the bloodiest campaigns ever. The Third Reich also invaded Russia through that border. So Russia, appropriately, does not want a transnational nuclear military, a military without any democratic accountability, a military originally staffed with former Nazi officers by the USA, a military that trained specifically to counter and invaded Russia, a military that ran Operation Gladio... Russia appropriately doesn't want that military to be developing its logistics, recon, fortifications, and nuclear capabilities on the border that Russia cannot effectively defend without massive and constant mobilization.

But the USA believes Russia is just going to have to deal with being under constant threat of invasion and nuclear strikes. That's why Clinton said, all the way back in the early 90s, that Ukraine would remain neutral - in public. And then immediately after in private asked his generals to draft plans for getting Ukraine into NATO.