You earn that right by winning games against the like of Brighton,Burnley etc not get trashed by them.
They have gone down before with players of the quality of Carrick,Defoe and Lampard
Carrick and Defoe were very young and Lampard was no longer there. They were too good to go down back then too, they did because of bad management (think it was Roeder).
If they are relegated this year Moyes will be largely at fault and it will be added to his list of 'achievements' since he left Everton. If they barely save themselves from relegation, it's not a huge achievement that he should brag about. Getting them to finish mid-table would probably be above par achievement considering the morale of the team, just keeping them higher than 18th will not be above par.