My mom is a rerider after 4 back surgeries. She does just fine W/T/C with no sitting trot. She does find sometimes that her balance is slightly decreased whether that be surgery or something else. She has fallen a few times and has always been able to bounce back. (no pun intended)
My first real experience with back pain was after I fell off my green bean in Late August. I could not sit in the saddle when I got back on him. (You always get back on!) I shoved it aside for a few weeks but come end of October after nannying...meaning picking up kids all day, I would come home and not be able to stand because of horrible back pain. I went to the chiro and had x-rays done. I was bulging my L-5 S-1 I believe. I was told not to ride for 3 months. I hopped back on mid-Jan. Walking felt amazing when I learned to relax and not hold my back still in a protective manner. The first time trotting was painful because I could not relax. I was so worried I was going to hurt myself again. I am back to riding 3-4 times a week. The only time I have trouble is when A) I get left behind when my greeny goes from fall-over-and-die trot to forward motion or B) The I'm-an-ex-racehorse before a canter trot. I have done some easy sitting trot that has felt ok. I do not do it for any length of time but when he is feeling up and gets prancy I feel ok sitting it. I've learned to two-point the canter to trot transitions and try to do more walk to canter transitions.