This boundary line is produced by extremely skewed distributions with very large values of one of the parameters and very small values of the other parameter.
Buried somewhere in our moral disapproval, our entirely accurate, clear eyed assessment of the skewed distribution of wealth, is an unholy fascination with the very rich.
The numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions.