Just tried the machine myself and it does indeed call it 1) NE 2) TEN 3) BAL 4) KC in the event of a 13-4 four way tie.
No point arguing what the first tiebreaker is, the rule is the rule, it's H2H/best win pct, full stop. So if the machine is not wrong then maybe what happens here is the Pats and Ravens tie for that first tiebreaker, then they move to the second one where the Pats win it therefore they're the top seed. Then with the 3 teams left trying to figure out who is the 2 seed maybe they move to the next tiebreaker since the top one was used already? I'd have to calculate all of that to know for sure but that would explain it.