I completely disagree. The whole body has to be outside the ring for it to count as being outside the ring.
I mean, unless you're a licensed referee (because all rules are enforced under referee discretion), it's not really a matter of opinion. If I have time tomorrow I can find the official rule book file I have saved on my old laptop.
Compare it to sumo though. Or football, or any sport with boundaries really. In most cases, it's not the whole body which has to cross the barrier in order to be considered a point or out of bounds etc (depending on the sport being compared to). The ropes in this case provide such a barrier.
If you want a real life example, look at the OSHA regulations for a confined space, which states that any body part which crosses the plane of entry shall be considered entry into a confined space.
Getting back to wrestling and this one specific example, had Becky just been able to pull Carmella away from the ropes while still in the submission, due to the no DQ format of the match, this would have remained a legal means of victory. Thinking about it logically though, if she wasn't able to pull her away from the ropes while Carmella had nothing to give her grip or leverage, she would have had an even tougher time doing it while she had a firm grasp of the rope.