I have never heard of this and I do not think that that NEC addresses the issue of being rated for support. It does state cable ties must be "listed as having low smoke and heat release properties."
That said however, here is a link to an article that discussed the Cable Tie "Type" Classifications afforded by UL 62275. Based on what I could dig up, I think your AHJ means 21S and probably has the authority to enforce it.
http://www.electricsmarts.com/industry/articles/view/17784
View attachment 12509
Your AHJ sounds like a wonderful person to work with. I would list him as type "DB" with a PITA rating of 10