No land based casino will allow just anyone to walk into their vaults to see if there is money there. Revealing anything of the sort is at the at the owners discretion.
"Land Based casinos" are quite a different story. Normal regulated casinos have to meet the governing body rules for amount of capital on hand during any gambling event. If they are audited and do not comply they will be shut down. The thing with regulated casinos, is, if you place a bet that they can't pay, the regulator must back it. That's what makes regulation nice. The regulator will go after the directors and take whatever assets they need so that everything balances out. This is why regulation works. The public can feel safe in the knowledge that some trusted party knows how much capital these casinos have.
In the bitcoin 'wild west' casinos the only regulation is the community. Bitcoin itself is a trust-less currency, but the business's attached to it are not. And to keep you honest we must interrogate your every move. You shouldn't be getting angry, defensive or insulting about it, you should encourage it. The community should be encouraged to question anyone running a bitcoin business. Indeed, it is not nice to be attacked, but the community will respond based on how you respond. I've run several businesses and it is common for customers and stakeholders to be rude and demanding. If you react unprofessionally you will indeed be attacked further. Take a look at all the companies Greenpeace attacks. The ones that respond positively to their attacks get better treatment. The bitcoin community is very similar.
But lets get back on track. The issue of not proving bankroll is still quite real. If someone gambles at max bet multiple times, then wins, and you don't have enough money to pay the big win, how will you pay it? It is expected you will pay it from the bankroll. But if the bankroll is not enough you are basically bankrupt. Being insolvent doesn't mean you can't pay out now, it means you can't pay out in the future. This is why the solvency question came up by many members of the community. In many countries, a company can become insolvent if its future liabilities might not be met, and this calculation does not include asset values which cannot easily be liquidated. This is why receivers come into companies before they become completely bankrupt or dissolved. Unlike the regulated world, if you don't have enough to pay, you just run off and become hard to track down. So still, without proving you can support paying a big payout, you are still providing concern for the players who really bet big. And that's probably why you only have dust betting and faucet betting. Big players are scared to gamble big because you don't have proof you can pay. It really doesn't matter that you say you can pay hundreds of bitcoins of winnings, to a player they need some reassurance that it will be possible before they throw down a bunch of 50BTC bets. And these big players are the ones you want, not the faucet players who just increase the bet count and cost you money.
Your business is about making the 1%, and you should be encouraging the big players to play so that you get more wagered amounts and thus potentially a positive cash flow.