I mean I could show a BTC address that regularly receives 5-7 BTC payments (I send them so I know it exists).  What mining power does that prove it has (it has none that I am aware of but does receive other transactions)?

Obviously if the address listed is getting 3 BTC every 10 minutes (and those transfers are directly from freshly mined coins) then it strongly suggests it has a bit over 10% of network hashing power but I sense that isn't the case.

EDIT: Let me clarify my point.  Right now my fund (LTC-ATF) has 77.209 BTC on Bitfunder.  If one of my investors asked me to prove it (which they are perfectly entitled to do) I'd screen-share, log in to Bitfunder and show them a balance of 77.209 BTC.  I would NOT show them a BTC address that had an incoming transaction of 77.209 BTC and ask them to accept that was from Bitfunder.  Do you see where I'm coming from?  There's a HUGE difference between proving you have X BTC and proving you have/had X BTC at a specific place/from a specific source.  Doubt anyone thinks Labcoin people couldn't RAISE 3 BTC (anyone with a net connection should be able to come up with 3 BTC in a few hours) - issue is whether they actually mined it.  And I'm not grasping where the proof is that it was mined - I'd happily stipulate that I agree they can control an address with 3 BTC in.