It doesn't make sense that they would take the level into consideration TWICE for to hit. (BAB and 1/2 to attribute)
Let's explore the other attribute option (1/3 rounded up):
Stats:
1, 2, 3 = +1
4, 5, 6 = +2
7, 8, 9 = +3
10, 11, 12 = +4
13, 14, 15 = +5
16, 17, 18 = +6
19, 20, 21 = +7
(I personally find this much more streamlined.)
Melee to hit is +7 for strength and +4 for 6th level skirmisher and -2 for two claws. Ranged is +5 and +4 for 6th level skirmisher.
There could be another formula for determining skills, with this creature getting a +10 to his spot in addition to that formula.
Doesn't explain the damages though, and personally I think it's probably the same formula as 3.5 plus 1/2 level. However, I still don't see why they would take the level into consideration twice.