Do web wallets keep customer accounts isolated?
There are different kinds of web wallets. Some are more like pieces of software that you re-download every visit, but you still actually own the private keys (re-downloading is still a risk, mind you). But in this case it looks like you're talking about an exchange or other web wallet where you don't actually own the coins anymore (i.e. they have the private key). Yes, in that case it's normal that coins are not isolated anymore. And yes, that is extremely dangerous and has gone wrong many times before.

In general try to avoid web wallets and if you really need to use for example an exchange, try to move out the Bitcoins as soon as you can, to minimize your exposure to this risk. If you're actually actively trading on such an exchange, then you don't really have a choice and simply have to accept the risk of losing all your coins one day.