Wow, are you stupid?
Their hand-to-hand skill almost means nothing. Especially not on the first floor where everything have low evasion and low defense. What makes MNK's pull ahead at start, and this is assuming no one have any cells unlocked (that means, pre-chest patch only), the MNK will outdamage the PUP because of higher Martial Art. Assuming they'd have the same Martial Arts level (which they don't), then yes, MNK would pull ahead of PUP. However, as it is, the reason MNK outdamage PUP is not because of their hand-to-hand skill. Their hand-to-hand skill is, just like WAR, THF and NIN, one of the reasons they're useful on the first floor. And before weapons etc. PUP will outdamage said jobs (notice how I didn't mention MNK there).
However, right now, post-chest patch, a MNK will always outdamage a PUP. Not because of higher H2H skill and Martial Arts level, but because they will most likely be your tanks. Thus, you gear them up first. this means they get first weapons, first equipment, first melee stat cells, first ability etc. Partly because you want them to tank on first floor because of Counterstance, which speeds the floor up by a whole lot.
However
If you gave the PUP the all of that first (which would be stupid, mind you), then naturally the PUP would outdamage the MNK. My point is, you can't ever compare job's damage in a situation such as Salvage, where most of the people will be partly unlocked, and some of the people fully unlocked, as they will lack stats, equipment etc. Especially on pet jobs, whose pets go under the same restriction as their master, and they are likely to not get STR cells before melee jobs. A MNK will outdamage all other jobs on first floor, including WAR and SAM. So saying a MNK will still outdamage a PUP in salvage is moot, as a fully-unlocked PUP will easily outdamage a completely locked PUP, and vice versa. The reason PUP don't get unlocked in Salvage is the same reason THF and many other jobs don't get unlocked. They are usually not a key job. MNK, WHM, RDM, THF and BRD are key jobs. However, the MNK is the only one that needs to be completely unlocked to be effective. MNK is a heavily geared-based job, which PUP is not. A MNK with only ability and weapon unlocked will be outdamaged by a PUP with only weapon and ability unlocked, simply because the PUP have his pet. The PUP, on the other hand, will never get said cells before a MNK, simply because a MNK is more versatile and important, while a PUP is replaceable. PUP, like all other melee jobs, take a back seat in Salvage.
I guess it depends on your group though. A WAR, or hell, even a SAM, could take a MNK's place in Salvage, assuming you have no MNK. A MNK will still be more useful, though, due to Subtle Blow.
I admit defeat here, since I shouldn't have talked much about salvage since I've never done it yet. Thanks for explaining, though.
PS: I don't have anything against PUP, I just think SE did a bad job at doing it, and *could* have made it good.