Clumsy phrasing comes from clumsy concepts. That's way too narrow a definition of the word "powers," and not in keeping with the tradition of superhero comics and movies. There's nothing about the word "powers" that requires them to be physically innate. Power is merely the ability to do things. And it can be granted externally, like how a judge has powers vested by the state. As Wikipedia puts it, "Similarly, characters who derive their abilities from artificial, external sources—the Six Million Dollar Man and his bionic limbs, Green Lantern and his power ring, and Tony Stark and his Iron Man armor may be fairly described as having superpowers, but are not necessarily superhuman."
My problem with the phrasing is that it implied that Mace's ability to be a hero is nonexistent or fraudulent just because he gets his strength temporarily from an artificial source. There are plenty of heroes who work that way. Not to mention heroes whose abilities are both permanent and induced by external technology, like Cap, the Hulk, Deathlok, etc. The only difference between Cap and Mace, ability-wise, is that Cap's "performance enhancer" never wears off.
There is another significant difference between Mace and Iron Man, Ant-man, Green Lantern, etc, though. They're all either in direct control of the technologies that give them power, or they're part of clearly trustworthy organizations that don't micromanage their members. Mace's powers come from the US military and - unlike Cap - are still directly under the control of the US military/govt., which could take them away at any point and give them to someone else, or give them to lots of other people without taking them away, etc, etc (depending on the exact nature, of course, which hasn't been fully revealed yet). Therefore he doesn't really have control over them, and could at this point still turn out to be nothing but a prototype prior to a much wider use of the serum as a weapon.
It's understandable that a situation like that could give rise to questions about the difference between 'superpowers' vs. just powerful weapons (hell, in another continuity Icers could count as a superpower, but here they're SHIELD standard issue). There does come a point where something can be so divorced from the individual that it's hard to count it as a personal superpower (ie, one 'Yellowjacket' is a supervillain, but an army of 'Yellowjackets' is just a really strong army).
Of course, Coulson was mainly just angry in the scene, not reasoning out the proper terminology for Mace's serum.