There's a wide gulf between "some customers may have trouble using Slack" and "most/all customers are completely unable to use Slack". Putting aside formality, I'd say "Slack is down" is in fact more accurate here (assuming that it is true that most users can't use it, which is true for our company at least).

Because it's not that you "may" have trouble

If their service is down, you will have trouble. The service will be absolutely inaccessible. Don't give people hope with "may"

But 1) it has apparently not been the case that the service was "absolutely inaccessible" and 2) "Slack is down" is still very imprecise and not a great alternative even if the service had been "absolutely inaccessible."

It was pretty clear the 'may' is a euphemism when your whole system is down.

To me it's mildly irksome in the same way as people who say "may or may not". Like, yes, those are the two possibilities, thank you.