In terms of proper protocol for a post-game interview, it usually goes like this.
1) NFL teams are made aware that the network doing the game (ESPN, FOX, CBS etc) will be looking for a post-game interview IF they utilize a sideline reporter. (CBS does not anymore during the regular season).
2) The interview will be live if there's time allotted in their broadcast window or taped.
3) The network (producer and reporter) will inform the team's media relations director they will be looking for an interview.
4) Sometimes, the team's media relations contact will say, "just grab the player of the game." Other times, they media relations person will say "find me or so...so (another media relations contact) and we'll coordinate and help you get the person."
note: I did see highlights of brady walking with Stacey James after the game but i was at the game and did not see what happened and since it sounds like it was a cluster bleep...i'm not surprised i haven't seen it again!
5) The reporter always has someone in their ear from the truck asking them..."Did you get him yet? Where is he? Do you have him?"
This becomes very rushed at times and that's where confussion sets in as well. Players also are talking to other players either on their own team or the opposition...and yes...the last thing they want to do is an interview right away but again, networks are sometimes pressed for time and they are "forced" to grab someone right away.
Like I said, I haven't seen the interview but someone asked for protocol and that's 99 percent of the time what it is. Hope that helps.