I completely agree with you. I pulled this from the NFLPA contract from 2006:

Article VIII Club Discipline-Conduct detrimental to club: Conduct detrimental to Club—maximum fine of an amount equal to one week’s salary and/or suspension without pay for a period not to exceed four (4) weeks. This maximum applies without limitation to any deactivation of a player in response to player conduct (other than a deactivation in response to a player’s on-field playing ability), and any such deactivation, even with pay, shall be considered discipline subject to the limits set forth in this section.

Article XI Commissioner discipline-Section 1 league discipline: Article (a) subsection (b) action taken against a player by the Commissioner for
conduct detrimental to the integrity of, or public confidence in, the game
of professional football, will be processed exclusively as follows: the Commissioner will promptly send written notice of his action to the player, with a copy to the NFLPA. Within twenty (20) days following such written notification, the player affected thereby, or the NFLPA with the player’s approval, may appeal in writing to the Commissioner.