If you sign up through a link from an airline, you will only get that airline (but usually several hotels) as an option. Similarly, if you sign up through a hotel chain link, you will usually get several airlines, but only that hotel chain as an option. They are promoting loyalty so wouldn't want your points to go to a competitor after all.

So if you want airline choices and don't have many miles in your existing account, close the current one and take up the Hilton offer. Or if you have more than one email address, you could always keep what you have and see what the new one offers.....