Well, you have no proof. Fuji can be an anomaly among the admirals.
You don't have proof that is he a logia either if anything the question should be what devil fruit type does he have zoan,logia or paramecia also the admirals have a theme Kizaru has logia, futitora is not a logia making the devil fruit power he uses a paramecia and the old three admirals had the logia theme plus THREE devil fruit types zoan,logia and paramecia this going very well with the 3 admiral spots also a zoan admiral would be cool since the admiral would actually be a strong fighter without having a overpowered devil fruit.
all the zoan fruit haters like you prove how much we need some more bad ass zoan fruit users sengoku had a zoan fruit but it was more about turning into a giant human buddah than a animal.
With jack the dog as your avatar i would think that you would like more bad ass zoan fruit users.
–- Update From New Post Merge ---
It's very likely that Fujitora hasn't eaten the gravity DF, but his sword.
And, what logia DF is left anyway ? What Oda could come up with now ?
I think we can both agree that the devil fruit power that fuijtora uses is more likely to be a paramecia than a logia since blackbeard darkness fruit is already the logia version since it has gravity powers of sucking people towards the user and it's the reason blackbeard cannot let attacks pass threw him.
the original admirals had the logia theme and with 3 admiral spots it makes sense one will have a fruit power of each type kizaru has a logia,fuijtora has a paramecia power it's possible that his sword might have it but because we have only seen zoan's feed to objects he could be using it like law uses his sword that leaves the final admiral with a zoan we have not actually seen a real zoan admiral before since sengoku's human model buddah just turns him into a giant human pretty much so not really a admiral it just goes under zoan so it would make no sense under logia/paramecia.
Maybe green bull is the one using a zoan devil fruit weapon and fujitora ate his fruit you would be correct about a admiral with a devil fruit weapon but you just picked the wrong admiral to have the devil fruit weapon i would be betting on green bull having the devil fruit weapon since he most likely has the zoan fruit.