"In March 1997, Everton manager Joe Royle brokered a £4.5 million move, with Bilić claiming he had a debt of loyalty to West Ham to stay with the club until the end of the season to ensure they were not relegated. West Ham finished in 14th place, two points above the relegation places."
Therein lies the difference really. If Payet hadn't refused to play, and at least had the decency to knuckle down until the summer before leaving, I'm sure Bilic wouldn't be quite so riled. But if he did still get riled in that scenario, then he'd be a hypocrite.