The ring needs to come off.

However, your bigger issue is that if the lock cylinder is freewheeling full
time, you will not be able to remove it with the stiff wire.

You will need to replace the lock cylinder AND the steering lock/housing
assembly.

The lock cylinder freewheels when a tiny cast tab breaks off.  The tab is
designed to break if someone tries to force the ignition, but they also tend
to break after years of use.   Once the cylinder is freewheeling, you cannot
turn it to align the pin hole with the catch, so the stiff wire trick can't
work.  There is no other way to get the cylinder out, so you have to discard
the entire housing.

Brett Anderson
KMS - Koala Motorsport
www.bmw-stuff.com