Ok. That is a pretty complex movement really. I also watched some crew rowing videos. Wow. I never really paid attention but I'm surprised you guys weren't hurt more often. I find there is hardly any literature on rowing related injuries at all. Although rib fracture is mentioned a lot. The back muscles breaking the ribs sounds like something the coaches made up to explain the problem to themselves, though. I doubt there is a known etiology for that.
The first thing I thought about was facet joint injury. But I doubt that very much since you said it went away at first and you were able to return to rowing but now it gets re-injured or re-aggravated often. This will sound as non-specific as your physio did but I think you sprained your back or you strained it. I.E. you injured some part of the superficial soft tissue and it's not spine related. It "healed" but it's on chronic hair trigger now. If you ever sprained another joint and then let it heal on it's own but had it acting up now and again afterwards you'll know what I mean.
More likely a strain than a sprain. Given the nature of that movement I can actually see a sprain but it's harder to sprain your back than to strain it. And since you were back at it a few days later that further points away from a sprain.
That makes sense if you think about the fact that you returned to rowing a few days after you hurt it and at first it hurt like a bitch, right? Too much too soon. There could be all sorts of complicated injury mechanisms but "you pulled something" is the simplest explanation. Now you've laid down scar tissue and have a vulnerable area where other surrounding tissues easily go into spasm. Just a swag but you know about OCCAM's razor, right? 
There are bound to be trigger points that are associated with this. That is something you can find and treat somewhat yourself. But for primary therapy I think some kind of good therapeutic massage may be the way for you to go. You need someone to physically lay hands on you and find the scar tissue, knots, trigger points, etc and begin working them out.
You said that the foam rolling hurt, right? Chances are you started with too hard a roller but the problem with rolling on an old injury site is that you start with a fairly hard implement and you can't control the pressure that well. When you assert pressure on the injury site, to the body, it is a lot lie strethcing the area so if it is too much you get the same pain response as you do with the triggering movements.
Any postural issue and assymetric range of motion problems you have can be accacerbating this. A therapist who could do manual therapy and also evaluate range of motion would be ideal. For self therapy on the back itself you'd want to use a tennis ball in a sock so that you could find the points that elicit pain and apply just the right amount of pressure to them and build up slowly from there. OR a theracane.
For upper body strength training I think you should focus on bilateral movements, at least for the most part. Funny thing is my gut is telling me that "rowing" exercises with a cable pulley machine would be good for you. Not to be confused with boat rowing. Barbell rowing I'd say no. But dumbell rows would actually be one unilateral movment which could be good. Learning and practicing perfect technique would be paramount. Also face pulls with a high cable (which are really a rowing movment to the face) and various other scapula related exercises. Wall slides I think would be beneficial to you.
Given your history check out the front of the body as well. Check the range of motion for you pecs, pec minors and anterior delts. If you have any of that hunched over posture we've been talking about I don't need to tell you that you have to start changing that. Keep in mind that postural issues can not be corrected by just doing exercises at the gym.
I'll stop short of writing a novel and wait for your response.
