Besides the skin tone being off, I think tinting it gray overall actually takes away from details and variation in tan and sooty fabric, etc. You've got a real firefighter in a uniform with real smudges and marks that got somewhat obscured by the gray. I did a quick search of photos of firefighters and looked at professional ones from newspapers/TV stations and a lot of uniforms are tan and you can see the variation of grimy jackets/uniforms. I think these got too overall gray
I noticed for example the first helmet where there are a couple of black marks on the white part around 'Captain'. I feel like it could better being able to see black marks on offwhite, rather than those being somewhat lost in the gray.
Now there is no rules that dictate that a portrait needs to depict actual colour and skin tone, it’s called creative freedom for a reason. The greyish tone is something that has been used for ages, whether one like it or not is and will always be subjective, personally I think it can have it’s merits if used correctly. In this case I think I contribute to an atmosphere that you would not otherwise get if OP had chosen a more natural colour scheme, a quick search on google on firefighter portraits also shows this.
Secondly using a smoking machine is going to influence on contrast and colour representation.