During that discussion they were referring to East Germany, not other countries. The meeting happened after the Berlin wall came down, but while the Soviet Union still controlled East Germany. And not even permanent prohibition of NATO expansion into East Germany ended up being part of the deal. When he went back to Moscow a few months later, he offered even less, that NATO would only stay out of East Germany during a transition period, and that once Germany was unified, all of Germany would be considered part of NATO. Gorbachev was ok with that.
Luckily, we don't need to debate what was or wasn't part of the agreement, they literally wrote it all down. Bush and Gorbachev met in person and signed the treaty which included the provision that NATO troops would not expand east into what was formally known as East Germany until all Soviet troops were gone in 1994. That's what the agreement was. What was offered during negotiations of the treaty (which isn't what you're claiming it was), but not included in the treaty, was not part of the agreement.
That is why Putin calls the West the Empire of Lies. Lying bastards, deftly manipulating facts for their own benefit. What can you negotiate with such people who say one thing, think another, and do a completely different thing? This will not work with Russia.
Even if the US Secretary of State told Gorbachev that NATO would never allow a country in Eastern Europe to join NATO.....so what? It was a negotiation, there was no formal agreement, the Secretary of State is not the US President and doesn't have the authority to formally speak for NATO like that. And even if he did, when they later made an official deal, which Gorbachev agreed to, it completely contradicted what was said in that meeting. The "not one inch" in the official 2 + 4 treaty was only until 1994, which was when Soviet troops were planned to no longer occupy Eastern Germany.