I think "modification" is a dangerous word because it implies that there is some sort of benchmark that you are not meeting. In almost every session I coach, I say some variation of "Whatever you can do today is exactly right." And I don't say that in order to be patronizing. I say it because it's true. If you are working with your maximum effort, your best form, and best energy, then you are doing everything correctly. "Best" doesn't mean "break yourself." We are looking for precise quality movement. But if your shoulder is bothering you, your best effort will mean leaving your shoulder alone. Training is not a competition. It's just training, no matter what anyone says. You shouldn't be injuring yourself in training. Competitions are competitive and sometimes you have to pull out all the stops in order to win. Training is just a chance to lay down another layer.
I'm not trying to give people an excuse to take it easy, but the goal of training is to be able to commit FOREVER. You are never going to finish fitness. You are never going to win exercise. You simply succeed by being consistent. And that means that, in order to stay with it, you are ALWAYS going to have things that you need to modify. And that's okay because the first step in learning to do something is to master the modification. So whether you are modifying because of an injury or you because you don't yet possess the strength/flexibility/stamina, know that the "modification" isn't a scaled back version, it's a step up that is going to get you a little further down your path. The simple fact that you are doing it makes it a step forward.