The -AP idea is just an idea. It could be for something else. The -AP cost switching from primary attribute to skill-boosting ability could indeed be too big a bonus and we'd be back at the older system which made skill-boosting abilities too alluring.
Skills currently do take into effect a weapon-cost minimum, which is why if a Ranger switches from bow to Crossbow, the AP cost for their bow attack skills will go up by 2.
The bonus is not for normal attack weapon swings, it is for adjusting the AP costs of skills. This means that the current AP costs for skills will probably go up, and yes, there should be a minimum AP cost for skills which won't go down.
For example, say the AP cost for Crushing Fist is 6 to start out with, and its minimum cost has been set to 3 AP. Even if I have Man-At-Arms 5, and thus the -5 AP modifier, Crushing Fist will not cost 1 AP, it will cost 3 AP.
However, High-Level-Big-Attack, has base AP cost is 11 to start out with because it is high level and powerful. A character with Man-At-Arms 1 who meets the level/attribute requirements can still use this skill, and it will cost 11 AP. A character with Man-At-Arms 5 - someone who has specialized in Man-At-Arms - (and who meets the level/attribute requirements) will get the -5 AP bonus for specializing and so when they use that skill, it will cost them 6 AP. If they have 4 Man-At-Arms (-3 AP), that skill will go down from 11 AP to 8 AP.
The idea is that you can still use those skills if you're a generalist (req's permitting), but a specialist in that area will get more benefit.
It's not a perfect idea, certainly. One issue which potentially ruins the idea completely is that before, it was gated by having an odd number of points into a primary attribute lower the AP cost, and so it could take up to 4 character levels to lower the AP cost by 1.
So it could indeed be that lowering AP cost just won't work there.
A pretty solid idea in my book. It adds a new requirement for using skills at their best. First a character needs to learn a new skill (which basically means having the skill book and the required level), then he has to invest some points in the relative stat and the relative "way of", otherwise the skill in question will be underpowered and too costly AP-wise.
Maybe overcomplicated, but it could work.