OP says that a lot of Philosophy makes use of the scientific method. An interesting point to bring up is that many Philosophers argue that there is no general scientific method. See Feyerabend's Against Method or, more recently, Steven Shapin's The Scientific Life: A Moral History of a Late Modern Vocation. Shapin in his book questions why we put science on such a high pedestal in terms of the authority it has about making statements about the world. I'll say right now that I'm not taking a skeptical stance and saying that scientists do not create any knowledge about the natural world when they do science, but we should be skeptical when people say that there is a general scientific method. A biochemist, botanist, physicists, and a behavioral psychologist all embody a scientific attitude, but their methodologies I'd argue are all completely different. Eg. The psychologist would probably use inference based tests that rely heavily on statistics while a physicist might use falsification or inference as their methodology. I think you'll find some philosophers, specifically the analytical ones, also have that scientific attitude.

So, where do they draw the line? There is no real line. It's probably not the best way to think about it. What can be said is that with the rise of the scientific attitude since the 17th century, many philosophers have taken a similar attitude when they do their philosophy. Bacon and Descartes are the obvious examples since they are essentially the progenitors of the scientific attitude. David would also be another example.

I hope that gave some insight into the question you're asking, chicken_chaser, because it's definitely an interesting one.