Let's look at this from the aspect of a normal bank account, after you create a bank account, you are given a unique account number, that only links to your bank account. And until your account becomes dominant this number remains yours and yours only.
You are right about how a bank account number works, but take note that there's a big difference between a bank account number and a bitcoin address.
Even in theory, it's impossible that there are two different persons with the same bank account number. The bank account number is given to you by a centralized service while your bitcoin address is generated by yourself and in theory it's possible that two persons generate the same bitcoin address.