People should be suspicious of statements regardless of tone. Conmen, hackers, cult members, job applicants, and AIs are all trying to trick people who only listen to tone.
Where's the operator overload? ;)
Whenever you see information that sounds like it could be extremely important to you and your situation (and when being wrong could really hurt you) then no matter how authoritatively the information was delivered that's really when you should invest the time to verify it. Much of the time that investment is just a quick internet search anyway.