If you compare the working seat mechanism with the faulty one it may be obvious where the problem lies.
The connecting mechanism can sometimes be quite crude , with simple rods etc. A rod may have popped out of its hole or some such, and it may even be possible to reconnect it without removing the seat.
A quick search on google shows about 3 'how to' videos on you tube for the Jazz/Fit.
If something has broken that looks beyond your skill to repair you may decide not to bother trying to remove the seat.
On the other hand if it needs repair it might help to remove the seat, or part of the mechanism, yourself and take it somewhere to be repaired. If they can see instantly it might only take 5 minutes to fix, maybe a quick blob with a mig welder to fix a bracket etc, they may do it there and then, especially if you are paying cash. And its not only garages that might have the necessary skills.
If they need to remove, investigate, fix, then replace the seats it becomes a whole new ball game in time, labour costs and scheduling in workshop space.