It seems the average rating displayed can be wildly different than their strength in that time control. Am I wrong?
It’s not skewed, you have different ratings for different board sized and time controls. See below:
Overall* rating. It is not an average of your other ratings, it is its own unique pool and you should not expect anything more than vague correlation between any two ratings. They are of distinct pools and thus cannot be compared between each other. Only comparing with the same rating of another person is possible.