I think you're missing the mark here. Psychiatry by and large isn't competitive. When we say "competitive," this often refers to things on paper such as class rank, board scores, research, etc. While psychiatry isn't really competitive (relatively) in those terms, there are plenty of other variables that can make it harder or easier to match, but we don't typically classify those elements as 'competitive' simply because as a medical culture we've come to synonymize competition with easily measured benchmarks (board scores, class rank, publications, med school reputation, etc.)
You can match into psychiatry much easier, but that doesn't mean that you're a shoe-in (is that even how it's spelled?) for any particular program. The program I graduated from was not "competitive." We weren't huge, academic or in a nationally recognized city. We had 5 spots. That leaves a lot of variability. We had a year where we went nearly to the bottom of our list. Two of the past three years we matched our top 5. There were a lot of other people wanting to match there but since the top people also wanted us, it didn't really leave room for anyone else. There also wasn't any correlation amongst the top of our list with regard to board scores or med school -- that's just the way it is. We've had people who were AOA at very well regarded programs interview who had 250+ step 1s and end up getting ranked in the mid or lower end of our list -- not because they were bad or that anyone didn't like them, just simply that there were a lot of other people we felt would fit better, who all on paper would be outmatched by these folks. This doesn't mean that being good on paper is bad, it just means that it's not as tightly correlated with matching at any particular program.
An analogy would be if you were a CEO of a Fortune 500 company and were seeking a mate. You likely wouldn't have any shortage of possibilities, but that isn't necessarily the same as assuming that any one particular person would love to have you, or that everyone would be dying to be your mate, despite having many more options than the rest of us.