That is not true. Once an ascent has begun, it will continue on it's own even if someone is overweighted. Try it. People who are severely overweighted sometimes have rapid ascents and subsequently have difficulty fine-tuning their buoyancy, causing them to yo-yo up and down. They don't have to kick all the way up.
It is true. The yo-yo you're talking about happens when there is expansion of air in the BC due to the depth changes. Remember, we were talking about a full BC at depth, there's no more expansion as one ascends, therefore the diver will stay negatively buoyant regardless of depth. Of course, as mentioned, there will be some buoyancy changes from the exposure suit (wet or dry) that may or may not be enough to make the diver positive as she ascends. As such, one would have to swim up to the point of neutral buoyancy or to the surface, whichever comes first.