At least on the prior generation of BMWs which had real ignition keys (and RFID interlock) and not just a fob you snapped into a holder, this isn’t the case.
Each BMW shipped with a number of keys (for example, mine came with 2 regular driver keys, a valet key, and a wallet key). The regular keys had the remote lock/unlock/panic buttons, the valet key would only open the driver door and start the car, and the wallet key was an emergency plastic key. All of them have the passive RFID for anti-theft, but only the regular keys could unlock the car remotely.
At the dealer level, the BMW system would only allow a total of 10 keys to exist for any given car. Keys are ordered pre-cut and programmed from BMW corporate. If you somehow got a blank BMW key and cut it, you’d get one that would unlock the cylinder but which wouldn’t start the car. In order to purchase an additional / replacement key, you are supposed to have to provide proof that you have the authority to do so (it is a bit more complicated than just showing the title, since the title may be held by a leasing company, but you get the idea). I have actually done this - I purchased an additional full-function key for my girlfriend some years ago.
Note that there are thus THREE separate mechanisms in place - the traditional cut key part used to rotate the door and ignition cylinders, the RFID used in the anti-theft, and the powered transmitter used for remote locking and unlocking. You CAN “introduce” new radio remote keys to the car (the procedure is in the owner’s manual), since the prior generation used removable batteries instead of ones that recharged while in the ignition. But they won’t start the car, only unlock it remotely.
If for some reason you need a key and that would take you over 10 (you lost a lot of keys, or some other reason), the dealer is supposed to require proof of an unencumbered title (no liens, etc.) in your name, and will insist that you purchase the keys as well as a new General Module (which, as I alluded to earlier, is the Spock’s Brain thing behind the glovebox).
BMW AG can reset the counter in the General Module and assign it a new code (otherwise, they’d have to scrap any that came back as part of recalls, warranty work, etc.) but that capability is not present at either the dealers or at BMW NA.