Perhaps you should check again.
I seem to recall that when Norwich sacked CH they were 5 points clear of the bottom 3, but after he left the club, Norwich only took 1 point from 5 games to go down. So if they had retained CH they may well have stayed up.
Too early to say without knowing what players are brought in or leave during the summer.
I do however have a feeling that the Bournemouth bubble could burst.