I've played around with the different scenarios, and this is true. Here are the tiebreaking scenarios (hopefully I haven't missed anything):
If the Pats beat the Bills this week, they clinch the division immediately (head-to-head tiebreaker).
If the Bills go 4-0 and the Pats 2-2 with the second loss to either the Jets or Dolphins, the Bills win the division (conference record).
If the Bills go 4-0 and the Pats 2-2 with the second loss against the Ravens, the Pats win the division (division record)
If the Bills go 2-2 and the Pats 0-4, the Bills clinch the division (division record tiebreaker).
If the Bills go 3-1 losing to the Jets and the Pats go 1-3 by beating either the Jets or Dolphins, the Pats win the division(division record).
If the Bills go 3-1 losing to the Jets and the Pats go 1-3 by beating the Ravens, the Bills win the division (conference record).
If the Bills go 3-1 losing to the Browns and the Pats go 1-3 beating the Jets or Dolphins, the Bills win the division (conference record).
If the Bills go 3-1 losing to the Browns and the Pats go 1-3 beating the Ravens, the Bills win the division (division record).
If the Bills go 3-1 losing to the Eagles and the Pats go 1-3 beating the Jets or Dolphins, the Bills win the division (common games).
If the Bills go 3-1 losing to the Eagles and the Pats go 1-3 beating the Ravens, the Bills win the division (division record).
Whew. I probably screwed up somewhere in there. That was a fun diversion.