Gil being created and entering the market that way is not the only thing that causes prices to go up.
When people's gil savings are distributed to players who want to spend the gil, there will be buyers with purchasing power (demand) that weren't there before. Player with excess gil saved up is not creating demand for items because he isn't going to spend the gil (it's excess). The poor player who buys that gil only buys it with the intention to spend it, and so demand for items on the market is increased.
Same amount of supply + more demand = higher prices. This affects everyone who participate in the market and not just those who want to RMT for convenience.