Hello; This has not been the case for me over the last four decades. From time to time, maybe once a year, I take my HOB's off the tank and give them a rinse with a garden hose. I am careful to not wet the sealed motor directly. Usually the hose will rinse out whatever happens to be in the filter.
I was intrigued when I first read about the practices of using tank water to gently rinse things such as the filter media and now the filter itself. I take it the idea is to preserve the beneficial bacteria (bb). This has not been a problem.
There are some ways to mitigate the bb question. First being keeping the established filter media wet, which can be put back into the filter housing after the filter is clean. Another is to not clean the siphon tubes at the same time as they should have colonies of bb on their surfaces.
A practice I have used for decades is to run some sort of air operated device in all may tanks along with a HOB. These devices (sponge filters, UGF's, bubbler operated HOB's and /or simply air stones will create some water flow. It is my take that the bb colonize many surfaces in a tank, not just the power filters, and will be on surfaces around water flow.
If my decades of experience itself seems not enough there is an article about cycling I can post a link to. In this article a small segments refers to the tennacity of the bb and that they are not easily rinsed away. Regardless, run your tanks any way you see fit and good luck.
Back to the OP's question. The heat of a dishwasher alone should be enough to ruin the filter. If the OP happens to give it ago, lets hope the results are posted.