Recent tradition in the NFL has awarded the opening game of the season, a stand alone Thursday Night three days prior to opening Sunday, to the Super Bowl winner. So when the Baltimore Ravens won the SB in February 2013 the baseball schedule was already out and it so happened that Orioles had a scheduled home game on what would be the NFL opening Thursday to kick off the 2013-'14 season. And since Baltimore also has a shared parking baseball/football area, the Ravens had to ask the Orioles to change their schedule. The O's, god love 'em, refused sending the NFL and their paid spokesmen (media members) into a major hissy fit decrying that some minor sport like baseball wasn't getting out of their way on command and breaking their long-running 'tradition' (it was probably less than a decade at the time) of the SB champ getting to lead off their season at home. The Ravens still got that lead-off game but it was played 2,000 miles went in Denver.
I suspect it's the other way around since MLB's September sked would be out months prior to football's so the NFL would know ahead of time which two (,maybe three) September Sundays the Phils would be at home and could easily give the Eagles a road game those days, or a Sunday night start, or one of the Monday/Thursday games that week. October would be tougher since everything on the baseball end is a constantly moving target so then it's probably MLB's turn to at least tinker with start times of games.