That makes sense Mr. L.
I would think that the physical attacks of your Pokemon would be based on your physical stats (Scratch, Tackle, etc.) while attacks like Flamethrower, Water Gun, Psychic would be based on Power. Since they are sort of like Pokemon spells.
What do you guys think? If their strength is just based on Power, that would be easy to only have 1 stat to determine how strong my Pokemon are. But I could see that being really rigged in my benefit. Which would be unfair to everyone else.