Individual contribution to PhD thesis as a part of bigger project
If it is acceptable to your institution, then it is acceptable. I think that in a lot of lab sciences people in a given lab collaborate with each other quite extensively to contribute to the overall goals. Doctoral theses arise in this environment just as you say. Some one (PI?) hacks off a piece of a larger problem and passes it to a student to develop and report on. If it has "acceptable" significance then the student has a thesis. Hopefully it also advances the larger goals of the organization. 

But this is largely due to the fact that, to do anything at all in such fields, that collaboration is required, along with the PI who provides the lab through grants. It can be quite different in other fields, but they have their own standards and processes. 



Of course, the student could see an opportunity for a smaller problem in the context of the larger one, just as the PI can. I don't mean to imply that it is always the PI that initiates it. Usually the student will check with the PI whether it is good to pursue the idea.