I agree that the real issue is the condition of the package on the date it was signed for and in that location. If the package was forwarded after that, not your problem and no way for you to prove it was or wasn't. The loop hole likely used by UPS and every other carrier which works in your favor here is the delivery signature. Somewhere buried in the fine print is boiler plate text saying that the signature is an acknowledge that the package was received in acceptable condition. If you want to make a claim for shipping damage you have to do so when you receive the damaged package. Obviously doing so a month later is suspect.

Pics of the items before being packaged is great but like you said doesn't prove their in box condition. Pics of the final box before it leaves your possession could help prove that any dents / holes / whatever happened later.

It doesn't really go to your original question but my practice is to pack things with the expectation that they will fall off moving trucks. Too many minimum wage, minimum intelligence, minimum give a damn bodies in the process. When they run full truck loads between sorting locations they run a conveyer belt in to the trailer and the load gets hand stacked tetris style. Just one opportunity for it to fall on the floor and / or get kicked around.