This statement is false, just think about it. Suppose there are two investors, A and B, and each have 50 btc onsite and 50 btc offsite. A is lying about it but B isn't. Why would A have -EBG but B have +EBG?
Great question.
These are the situations of your two investors:
* A has 50 BTC in total, it's all on-site, but he lies about having another 50 BTC offsite just to get more exposure to the action. He is willing to risk 2% of his 50 BTC on every bet. He's risking 1 BTC per bet of his 50 BTC.
* B has 100 BTC in total, He is willing to risk 1% of his 100 BTC on every bet. He's risking 1 BTC per bet of his 100 BTC.
Immediately it should be obvious that A's position is riskier than B's. A is risking 2% of his bankroll on the first bet, whereas B is only risking 1% of his bankroll.
The "realness" of your offsite has nothing whatsoever to do with whether your onsite will go up (+EBG) or down (-EBG).
But we're not concerned with whether our "onsite" grows. We only care about our net worth. (EBG = expected *bankroll* growth, where "bankroll" means "coins you actually own"). In A's case his onsite is the same as his net worth, whereas in B's case his net worth is the sum of his onsite and offsite. I think that's the point you're missing. As A loses his onsite he risks an ever increasing percentage of his net worth until he ends up being margin called. As B loses his onsite he tops it up with the coins which were offsite until now, and avoids the margin call. A goes bust, B doesn't.