Of course. I'm not suggesting having little distance between your green screen and subject.
Lighting to match your background plate is extremely important to getting your key to sell. Lighting your screen is extremely important to getting a good key. Creating distance and using light modifiers and grip equipment to eliminate green spill as much as possible, as well as creating some separation through lighting is also extremely important. Of course, this is of little use once you've already shot (and cannot re-shoot if there are problems), but all important to keep in mind for when you're approaching shooting and comping green screen. I never gave a specific number as to how important lighting is for green screen work, but it is extremely important. The worse your capture, the harder your compositor has to work, the better their skills need to be, and the more likely the output is to be sub-par.
Lighting to match, exposing the screen correctly, and eliminating spill are pretty much the three most important things you need to concern yourself with when shooting green screen.
Personally, I would have thought that suggesting you're unlikely to ever get a key to work in Premiere or AE (despite much evidence to the contrary) is not particularly helpful or insightful in a thread specifically asking for tips on Premiere and AE, though you're right - both Fusion and Nuke are perhaps better suited to, and more widely used on professional compositing work.
As for advice for the OP, this is good general advice:
Color correction is extremely important. Where you apply lightwrap (And where you don't) will really sell the composite.
Matching the grain (or noise) will help.
Environmental elements- dust, light leaks, chromatic aberration will also help.
Edge blur and pixel spreading helps.
If we can get a screen grab, we will be much better placed to provide specific advice.