A low margin business means that your competition will have extreme difficulty lowering their prices.
However, it's very rare for there to be fundamental, physical limits to the internal cost of doing business. Which means that if you can do that better (through manufacturing improvements, supply-chain improvements, what-have-you) then you can undercut your competition only slightly while reaping significant profits.
And, because your competition is running on such low margins they can't easily compete with you. So, from a pure price perspective, you either get to retain your higher profit margin while being price competitive or you simply eat the majority of the market before it has a chance to settle to a lower price-point, which is win-win.
It does, however, mean that you need to put in a lot of hard work.