Correct. I just wish there was any easier way to tell what airlines accepted - time wise.
Here's my take on timebuilding. No matter if a particular airline accepts safety pilot time or not, you're not hurting yourself to do it.
Let's say you go rent a twin for 50 hours, pay full price at $200/hr, and do all the flying yourself. That would cost $10,000. The 50 hours would most certainly be looked at as legitimate to any airline.
Or, in a timebuilding program, you could pay half the rate ($100/hr) and get 100 hours for $10,000. You would get 50 hours of time for yourself and 50 hours of safety pilot time. The 50 hours of time for yourself would definitely be legit. The 50 hours of safety pilot time may or may not be accepted.
So, in either scenario, you're paying the same amount ($10,000). In both scenarios you get a guaranteed 50 hours of legit time. In one scenario you get 50 hours of safety pilot time thrown in for free, you might say. And remember, even if the airline you want doesn't accept safety pilot time, you're still getting the experience of being in the twin, flying cross countries, working as a crew, etc.
My point is that if you're going to buy time, a "timebuilding" program is still a better deal than renting on your own, no matter what your future employer thinks. If they take the safety pilot time, it's icing on the cake. See what I'm saying?