This answer is, unfortunately, not correct. There is no reliable experimental evidence to demonstrate that a primary carbanion is more stable than a secondary carbanion. In fact, the opposite is true (JACS 1989, 1968). And neither carbanion would be stable enough to be formed.
So, what's the answer? I would honestly say that no-one knows for sure. High level gas phase calculations reproduce the experimental outcome, so it's unlikely to be due to solvation.
It's a little unfortunate that this has become a textbook example, since the textbook explanations do not withstand scrutiny. Please understand, I am not criticising the person who responded. It just seems that this reaction is a bit more complicated than it seems at first, and (in my opinion) it needs a bit more work to understand it.
Sorry if this response is not very helpful, but it's better to tell the unpalatable truth.