Yes I believe it is entirely possible to do your EE in your SL subjects. There are no IB regulations that prevent you from doing so (you can even do an EE in a subject you don't study, as long as it is an official subject offered by the IBDP), and if teachers say otherwise, you should mount your case.
I honestly don't agree with the idea of forcing people to do their EEs in their HL subjects. I mean, yes, it would be preferable, but in no way should doing an EE in an SL subject disadvantage the student.
Just because you take the subject at SL, doesn't mean you are any "dumber" at that subject! Take English, for instance, just because you take it at SL doesn't mean you have poorer analytical or linguistic skills. The SL/HL delineations are there for other purpose, and not merely to limit what you can and cannot do your EE in. Even if you took English HL, your EE is not likely going to overlap what you did in class!
Moreover, the EE guide states that the content and investigation of your topic should be more substantial than what is covered in the syllabus of your chosen subject anyway. For subjects like Group 4 (sciences), anything that lies squarely in the confines of the syllabus would be considered too trite for an EE topic. You would not score highly for the last criterion (Holistic) if you do so. In brief, if you were serious about your EE, your investigation should exceed the expectations of both SL and HL at that subject.