If someone damaged my car (and they did), there is no way I would accept a DIY repair.
That all depends on the inclinations of both parties in the accident, and willingness to pay insurance deductibles.
If a person feels confident they can restore the vehicle to total pre-accident appearance and function, they should probably do it that way. If they can't or won't, then they should pay the piper and have a body shop do it.
What I see in those pictures is one bumper that needs some rubbing compound and elbow grease, and another bumper that maybe needs a socket wrench and a half-hour's time re-seating a vinyl bumper.
I've mentioned my own '95 Trooper enough in other threads. I bought it as "pre-owned" or used. It had 95,000 miles on the odometer, and I paid $20,000 less than the original owner. I did not arrange for full-comprehensive coverage in my insurance policy. Three years later, I was in a crowded bank parking lot, checked my mirrors, and started to back out of a parking space. I could only eyeball one mirror at once, and at that very moment, another customer opposite my parking space also backed out. I can't even remember if one or the other party was determined at fault, but I didn't file a claim on my own car. A body shop provided an estimate of $1,100 to fix a damaged tail-light lens and a crease on the corner of the left rear quarter-panel. I think I had $500 deductible as my policy terms.
I first repaired the tail-light lens with the three-color parts-shop kit of plastic rectangles for $10 and a $4 bottle of super-glue. I had to call someone's attention to the lens repair before they could notice it. I later replaced the lens with a $50 order from an online junkyard. It was as good as new.
The crease in the quarter-panel required a cheap $25 slide hammer, my drill and bits, a $10 can of BONDO, $5-worth of sandpaper, and $30 in paint from Paintscratch.com. Masking-tape and newspaper are off the radar of any cost-accounting.
Add in some proxy for my time, but it was leisure time and not an equivalent of paid time. Maybe it was 10 hours, but for someone who had done the same job several times, at most 3 hours. Then compare the approximate $140 I spent overall to the $1,100 estimate. Under those circumstances, it's difficult even to justify my insurance company paying a body-shop the latter price.