I've had this same issue. I have a herniated disc at L5/S1 that can be aggravated by squats. I can dead lift just fine though, and can do a few single leg pistols....so thats how I get by. Last time I tried squats I was very bad off. Pain radiating into the leg and foot and couldn't get to standing upright. What I did:
1. Chiropractor - 3x/week for a month moving into home exerercises and rehab the second month.
2. No heavy weights for 2 months
3. Lots of low and slow activity (walking) and the specific exercises
4. I just stopped doing squats. My injury is an old wrestling one. Top loading the spine may be fine in the context of a relatively healthy person, but its not for everybody. I do leg presses (modified to eliminate any rounding), dead lifts, and throw in some pistols.
Good news is I avoided surgery going the chiro route. I've had this happen only twice in 20 years since the original injury. They wanted to cut back when it originally happened. Avoid surgery if at all possible! Anyhow, just throwing this out there as my personal experience. Having a back injury sucks, but there are ways of healing and strengthening. Don't let anybody tell you that you "HAVE" to do any one particular exercise. Its bunk.