This sounds absolutely wild to me. I've never heard of this. Version numbering should supercede release date IMO.
That said, Fortinet products almost always have a prescribed upgrade path. Please review the one for FortiClient (i'm surprised TAC did not share this with you):
As you can note from the document the official upgrade path from 6.4.X is direct to 7.0.7.
I would get back in touch with TAC and tell them their official documentation states you can upgrade to 7.0.7 from any release of 6.4. I wouldn't settle for no here. It's ridiculous to say you can't upgrade to version 7 because your version of 6.4 has a newer release date.