Whats strange about that? it happens all the time. Its not just a money or club stature question, if the coach and the club dont agree on what the objectives are, and how to get there, they dont accept the offer. For Allegri, Arsenal was millions of pounds in the EPL compared to his current unemployment.
Conte at Juve was getting paid millions and then quit because he didnt agree on the project. He chose to leave and become unemployed because of the details. He didnt just say oh I am so lucky to be working at Juve and making good money. Conte spoke out at Chelsea too when he didnt get the resources he was promised and got the sack.
Mourinho spoke out about the UTD management not giving him the resources too and got the sack. He didnt say oh my I am so lucky to be at the richest club in the world I will shut up and ride this while it lasts.
It happens in business too outside of football. You don't just gush over an offer from a big company if you think the targets they are setting for you are unrealistic. Thats career suicide. Getting hired at a big place, earning a few good months of salary and then getting sacked is very short sighted. You have your credibility and your career beyond that contract to protect.
And if its a leadership position, if the leader/coach is not convinced of the objective and the plan, that will transmit to the squad and the failure will be double. So yes if he gushed over being offered a Juve job and accepted it despite not believing in the plan, then its definitely his fault ..even more so than management's.