Well I don't know about WDW because I have never been there. However, you heard wrong about Disneyland. I went to a park meet on Stupid-bowl-Sunday and it was like any other Sunday in January.
The only way it might be more crowded is if it's unseasonably warm. I went to the January 13th meet and it was 80° and I'm guessing that must have been why it was crowded.
There are two myths about stupid-bowl-sunday
1) the park is dead
2) So many people go to the park because they all think that the park is dead
When I go to Disneyland, I tune my FRS Radio to channel 2, without a quiet code. They're faster than a cell phone and you can talk to a whole group at a time, and you don't have to get everyone's cell phone number in advance.
I went on Superbowl Sunday the year it was in Tampa last - 2000 or 2001 (I got the hell out of Dodge... traffic heading west on I-4 into Tampa was backed up big time, but east bound towards Orlando was a breeze). Went to MK and if I remember correctly, crowds weren't too bad and were pretty manageable. But back then I didn't like football. Now I watch it every Sunday during the season.