From the link which you posted:
Later that day, at a meeting with Soviet President Mikhail Gorbachev, he acknowledged that "It is important for the Soviet Union and other European countries to have guarantees that if the United States maintains its presence in Germany within the framework of NATO, there will be no extension of NATO's jurisdiction or military presence by a single inch in the eastern direction". and, in addition, he asked Gorbachev whether he would prefer a united Germany "outside NATO, completely independent, without American troops, or a united Germany that retains ties with NATO, but with a guarantee that, that the jurisdiction or NATO troops will not extend to the east of the current line." When Gorbachev replied that "the expansion of the NATO zone is unacceptable," Baker agreed with this.
It's clear that there was no written agreement about NATO not expanding eastward but her (Julia Loffe) claim that promises were all a fiction is not a serious argument - plenty of records in the link you posted.
Regardless of the above, I fail to understand why anyone would think that expanding NATO towards Russia's borders, considering it was Russia's mortal enemy throughout the Cold War, is a good idea.