There is no PDGA rule requiring three, or any other number, in a division. Here is the rule:
A Tournament Director may, by giving adequate public
notice, restrict the divisions offered. Absent such notice,
the director shall offer for competition any division which
has four or more players that are eligible and wishing to
compete. Tournament Directors may offer divisions with
less than four players at their discretion.
I'm probably not the situation that caused you to bring this up, but I'll let you know anyway. I played in a division by myself this year - which by the way, isn't like the TD sends you out for your rounds solo. You're competing in a group. It was explained to me that you should be able to compete in any division for which you qualify. I qualify for AM Grandmaster, so that's what I sign up for when I get there. I know there were a couple others that that day qualified for my division that chose to play in other divisions. That's their prerogative and I don't have a problem with it. I had two great rounds with Masters division players.
I am not a dues paying PDGA player (except on that day or two a year when I pay the extra $10 for PDGA sanctioned events), so I'm not working for a rating. I know what my score is, and what the scores are in my groups, and the other divisions. I'm competing, but I'm also there to learn from others I don't usually get to shoot a round with.
A valid reason to play in a division of one, is if the event is part of a "Series" of events. Like the So Cal or Nor Cal Series, the MST - Minnesota State Series or the Wisconsin Tour. Many "Series" will only give you points for the division you play in - not the division you "belong" to. So if I am in the running for a Pro Master Series title and I play in Open, I get Open points that will not go towards the Master's title. (This is unlike the PDGA - where all points I earn go to Grandmasters even if I never play a single event as a Grandmaster!)
So just because a player doesn't have competition this weekend, doesn't mean they don't have competition.