If OgNasty entered into either selling a short OR a PUT option then it would have no effect on number of outstanding shares.
Easiest way to think of it is that it's a bet (below is very simplified) -
OgNasty bets that NASTY shares hold their value, the other side bets that they lose value.
It's really nothing more than that.
This is a good explanation. Me willing to sell PUT options is only a bet that the share price is currently undervalued, and it's a bet I would be making with my own funds. The only effect it should have on shareholders, is to inspire confidence that I'm willing to bet the share price will go up.