The decision of whether or not private chat occurs in that situation is up to your company though, not the company you buy the water from. This policy change by Atlassian shifts the ability to set policy where it should have been in the first place (as they've noted): to the company purchasing access to HipChat.

So set a policy that you won't read their messages. There's nothing new here.

It's nothing but a policy that prevents your SaaS provider from reading your data in the first place.

Employees don't generally have to worry about their SaaS provider having an impact on their performance review, paycheck, or continued employment.