Yes, they can be soloed!
The 'links' around there are all EP, very easy to clear an open camp. Pull Headhunter into it - he's only level 45!!! Forget the local pets, at 45+ fungie will make a huge hole in his HP.
I duoed him yesterday with a 50RDM (I'm 45BST on my 2nd character) and we were both at full health when Headhunter went toes upwards. The RDM had to log, but I went on and soloed Gascon (he's only level 40, so a DC to me) and took him down with no trouble at all.
When I started on Gascon, fungie was almost dead but at full TP, so good for a final sic before I popped another fungie! Total fight time was probably less than a minute and I was lucky enough to grab him and pull him away from other links.
Trust me, these guys are very soloable, and can be a fun fight! Think of this as a challenge, clear the area first and you will have no problems at all!

CatrinM WHM75/
BST75/BRD45/BLM37/PLD37/WAR37
Bastok [10] Sandoria [10] Windurst [9]
Linkshell:
PromathiaChained / Shiva Catrin BST75/WHM37/BLM31/SMN9/NIN7/MNK6
Bastok [6] Sandoria [1] Windurst [1]
Linkshell:
PromathiaChained / Shiva Beastmasters never die, we just get do-overs!