You tell us Russia wanted to join the Nato and the US rejected that? That's a steep claim, any sources for this?
Discussion
To join NATO a candidate country has to officially apply for that and all the members - not only the US - have to agree. That never happened and such the US never rejected that. See also the process when Sweden applied for membership and Turkey first signaled to disagree.
The above thing is just a story that Putin tells.
Perhaps. But I haven't heard Clinton repudiate the now publicly known story.