Tom,
I looked up cable ties in the UL White Book. If they are listed ties, then "the evaluation of these products include consideration of the rated mecanical strength, maximum operating temperature, smoke and heat generation,corrosion resistance and weatherability..."
There is a requirement that the package be marked with the maximum load and thermal rating. The label on the one package of listed ties that I have is mostly missing & the only thing that I can make out is "suitable for use in air handling spaces" so I can't testify to a load rating in pounds. Seems to me at least some of the cable ties should have adequate strength to hold an MC cable or NM in place.
Anyhow, since you now know what this inspector expects, it probably wouldn't be worth fighting about.
Tom