No, the company doesn't control the share price. (think of the crazy scams that would create :) ) The MM's control everything; however, if a company has a solid business plan, and profits to back it up, the pps is bound to rise. You really can't manipulate that.
....but....and this is all my opinion.....
if the pps is at say 10 cents....and that is the actual price without manipulation. the MM"S can manipulate that price within a reasonable deviation.....say.... 1.5 - 2 cents (and i'm just picking these numbers out of thin air).
They do that to create what seems like MOMO and what seems like panic....in order to make money. But when it comes time for the company's next business move, the stock has to go up, as long as it's a solid business move. That's how I see it at least.