I don’t think most clubs think that way. Changing manager is always seen to be ‘doing something’ even if it is brainlessly reactive and ultimately counterproductive. There seems to be little account taken of the quality of the opponent or lack of money spent (the latter of course being the owners’ responsibility.) If Bournemouth had lost 9-0 to another promoted club it would be real cause for alarm. But this loss, while bad, is much more understandable in context. Everyone at Liverpool were furious over the result at OT and spent the entire week getting amped up to make a response. Bournemouth were unlucky to face them then, just as Liverpool were unlucky to take an injury-hit squad to OT the week after Man Utd suffered their own humiliating loss and had to respond.Something must've happened behind the scenes with Parker and Bournemouth — pretty harsh to dismiss him after facing three of the top teams in the league in a row. They didn't spend anything after earning promotion and always seemed a safe bet to go right back down again.
Firing managers in these circumstances doesn’t, IMO, represent ‘joined-up thinking’ as the phrase goes.