If you mean, how does one audit your addresses with block explorer, simply check the addresses that you have to make sure that there have been no transactions that you didn't do yourself and that the address balances add up to what you should have. If you have more than what you should have, then the website is sharing accounts among users and tracking the individual values internally. Which would allow the website owner to loan out portions of the pooled balance, much like how fractional reserve banks do now, since they don't actually keep your money on hand. If there has been any transactions in or out of said accounts that you didn't perform, then that means the website owner is using member accounts to "float" his own activities.
Bitcoin shares balances among addresses, so you'd have to modify Bitcoin to achieve this separation.
I had made the assumption that they already had. One client with one wallet.dat would be fine if the client was modified for multiple independent users, and sets of addresses were linked to a user and not assumed to be one person. That's a very Windoze like mentality. For that matter, there should be a GNU/Linux version that plays nice with multi-user systems, where the wallet.dat is in the user's disk space.