> The increase in value of a F9 booster after use is more than the near-negligible per-launch maintenance cost.

Do we have anything proving this besides the self-serving word of a privately owned company?

I'm not saying it's false, I have no idea either. But there's a lot of highly specific speculation going on here, based on no reliable source.

Yes, insurance rates for satellites launching on reused boosters go down the more flight tested the booster is.