It's a mistake to think of those as "your" addresses.
Your addresses are exactly those for which you control the private key.
If you had the private key of "your" deposit address on an exchange, you could "undeposit" coins as soon as they were credited to "your" account. (Note, its not really your account either - it's an entry in their database and they probably reserve the right to terminate it at any time for any reason).
Thinking of balances on exchanges as being "yours" is what leads to people losing huge sums when the exchange has a leak in their cold wallet. Or whatever.
So true.