The same executives said they hadn't heard of a suspension with pay before, and they said it smacks of being a public relations ploy.
Players are usually suspended without pay. Mays was fined $50,000 but, since he makes $205,882 per week, he will make $155,882 on Sunday.
The NFL said vice president of football operations Merton Hanks determined it was the appropriate discipline for that incident, and declined further comment.
Schaub's helmet flew off after the hit by Mays and the quarterback grabbed his head with both hands. He had blood dripping from his ear and missed one play. After the game, he said he lost a chunk of his ear but was otherwise OK.
Mays insisted he wasn't trying to go at Schaub's head and said he apologized more than once to the Texans quarterback for the hard hit.
Information from The Associated Press was used in this report.