I think you are still misunderstanding the term "placed".
Typically, a tournament will have prizes for the top ranked players. For example, a tournament might award prizes to the top 3 players (1st, 2nd, and 3rd). Another tournament with more players might award prizes for the top 5 players (1st, 2nd, 3rd, 4th, and 5th). With the Tournament Director software, you would award these by creating prizes that are assigned to specific ranks. A prize for rank 1 (1st), and prize for rank 2 (2nd), and so on.
When you use the term "place", as in "Did so-and-so place in the tournament?", the question is referring to whether or not the player got one of the top ranked spots, which is different for different tournaments. For the first tournament mentioned above, the player "placed" if they got 1st, 2nd, or 3rd place, since those are the ranks with prizes awarded to them. In the second tournament mentioned above, a player would "place" if they got 1st, 2nd, 3rd, 4th, or 5th.
The software defines "placed" in exactly the same way. If the tournament in question has prizes for ranks 1, 2, and 3, then players who achieved rank 1, 2, or 3 would "place". "Placing" does not distinguish between 1st, 2nd, 3rd, 4th, or 5th place, or any other rank. If you got the 1st place prize in a tournament, you "placed". If you got the 5th place prize in a tournament, you "placed".
So, for example:
A player plays in 5 tournaments
Each tournament awards prizes for 1st, 2nd, and 3rd place
The player ranks 1st, 6th, 3rd, 10th, and 5th in those tournaments.
The player "places" 2 times (when he got 1st place and when he got 3rd place)
2 / 5 = .4
Therefore, for this player, "Times Placed" is 2 and "Average Placed" is .4
This player "places", on average, 40% of the time.