Lithium ion batteries are basically a bit dodgy to start with. They have a few features including built in electronics to make them safe.
There have been cases of fire and major recalls with branded batteries but I guess the risk of getting something of poor manufacture is greater with the generic batteries.
Another argument against the use of generic batteries is that there may be warranty problems if an equipment breakdown could be attributed to an "original" battery.
One more can be that they may have a shorter life and/or not perform as well. One may consider though that even if these problems do exist, the difference in cost more than compensates for this loss.
Personally, I do use a generic battery in both my Pentax DSLR and Fuji bridge camera and have had no problems. That's just me though - someone else may reasonably prefer to avoid them.