I know some people will draw parallels with satoshidice, but that is incorrect because with satoshidice the owner actually keeps your bitcoins in return for passing on the risk to you of a non-performing website (in other terms, he trades the revenue stream in the future for bitcoins now).
However, with bitcoin exchanges accepting deposits. The deposits must be returned and therefore there is no benefit to the owner. Some have theorised that the coins deposited are used for prop trading. However, if this is the case, then it is possible that the website would have to close if the owner, who was prop trading, was to generate a loss. You never know, it might even be invested in a bitcoin ponzi...
The problem is the owner gets no benefit from paying interest as it eats into the transaction fee profit that the owner would otherwise have earned. So, unless they are risking your deposit it is very unlikely by merely having deposited your coins at an exchange, would they be able to make money, in which case the site will almost always eventually turn out to be a scam.
Exactly as you said.
Be extra careful before putting your bitcoin in such sites.