What's "hilarious" about a site being down?
In IIS this is a "last resort" error when even the custom error handler cannot respond.
But in this case for all we know it could be a software defect from which there is no recovery. IMO it's bad to overdesign recovery mechanisms that just end up masking design errors. Clever staged rollouts of changes are good ways to mitigate the impact of a new regression.
If someone accused me in person of being "disingenuous" during an honest conversation, I would find it pretty rude.
Most companies have some sort of static 'technical difficulties' page to redirect you to instead.