Most likely not.

That's not much the logic followed by movie makers or even studios. Not with someone like Jackson who would have raised hell (publicly) if execs forced him to change the plans just to make more money.

This sounds far more likely to be an editing issue. One of the movies as scripted ended up not working as well as they thought it would when they wrote them and the further they advance in the process of completing the movie, the more it bugged people involved. Rythm or length problem, or perhaps even dramatic one (e.g.: something felt far from optimal with the climax of movie one, or they had problems fitting all the build up to the final climax material in movie two and make its pacing work) They tried to trim it down or to solve the problems but were still not satisfied. Then at some point someone decided to try to move material from movie 1 to movie 2 and have the climax material of movie 2 stand one its own as a third - and that solved their problems. It may also be that both movies were just too long and the director eventually gave up on trimming them down, realizing he was butchering it and it was getting to hectic or fast-paced. In any case, the production had to sell the studio and investors on the changes...

They stand to make more money out of this, but that also increase the risks (they commit to an increase of at least 30% to 50% of their marketing and distribution costs for the project, notably. It could be more if the first or second movie isn't as successful as hoped and they need to push the second or third harder). Changes like this also has a significant impact on post-production costs. The risks aren't that huge considering it's prequels to the massively successful LOTR trilogy, but it's not a decision a studio would applaud to and greenlight automatically either. If the first movie unexpectedly disappoint and barely meet its costs, they stand to lose a lot by having split the two movies to make three. The new cuts presented to the studio had to be convincing.