This would cancel out the ~Stale label addition, because then the next
time the bot runs it would cound that as activity and delete the
label.

An example of this is visible here:

team#40409 (comment 2763207)

We would need some custom code to check the author of the action and
ignore the triage bot. I can't be bothered to write some Ruby right
now, so this is the simpler way.