As soon as Marcos Clutterbuck posted his response, I smiled, because I realized I've been silly to pride myself on my four hole-outs for eagle as being rare for someone who's never had a hole in one. I'm certain he is right that it's all about the number of opportunities you have for each.
Go along with opportunities.
I'm on 4 x hole-in-ones but have only ever holed 1 full shot from the fairway for an eagle.....less opportunities for shorter hitters who can't reach some par-4's in regulation (and have no way of reaching a par-5 in only two shots for a 1 putt eagle).
Atb
You're very right that it matters greatly what kind of player you are and what tees you are playing, which I thought was the flaw of the original assertion by the OP's club pro.
I'm a pretty decent player and decently long and it's pretty typical for 3 or 4 of the longest iron shots I face in a round to be on the par 3s. In my most recent round, the clubs I hit into greens broken down by hole par were as follows:
Par 4s:
9i, PW, PW, PW, 9i, PW, GW, GW, PW, GW, 8i
Par 5s:
PW, 9i, PW, 5i (second shot)
Par 3s:
9i, 6i, 8i, 7i
So it makes some sense when you look at numbers like the above that I've holed out from the fairway a few times but not made an ace.
For other players based on the course and tees they play and their length of driving the ball, those figures may work out totally differently.