I agree with that. In my experience the following make no difference to the op-up chance:

- booking class (including award classes - I've had many op-ups on award tickets)
- on-line check-in (or not)

These do:

- MPC status
- OW status
- travelling alone (or at least with no-one else on the same PNR)

And the key thing is: unless it is a special occasion op-up then the class you are booked in must be over-booked for you to get one, regardless of status (up to DM at least, not sure about DM+).

Special occasion op-ups seem to be considered:
- if you travel on your birthday
- on the first flight after renewing status (at least for Diamond, not sure for lower tiers)
- on passing a Club Mile threshold (e.g. 1M Club Miles)