Properly done photos can prove a damn lot. Show the hardware, show the mining software running, show the account at a mining pool, get the mining pool owner to verify it, make a large enough amount of hashing where faking it with gpu would be terribly difficult to do, etc.... What is so hard about it? It would be fun and amazing.
Their excuse would be not mining on the main network, but you could probably get a pool operator to set up a testnet-in-a-box and point a temporary pool-in-a-box at it. They could then verify the hashrate from the photos.