I have several thoughts regarding your situation with ECI. First of all, so many 3 year olds, and under 3's especially, would be a little apprehensive, cry, and possibly not want to engage with people they don't know. That, to me, is developmentally appropriate, and if you were feeling any anxiety at that meeting, your son may have picked up on that also. If he did, that's okay. Just be aware of your own feelings when you go to meetings like that because many kids are sensitive to their parents' feelings.
I think that sometimes professionals are very quick to slap a diagnosis on a child to explain certain behaviors and reactions. Even as a former counseling professional, I think that. Some diagnoses take multiple assessments to determine.
My son, who is 2 and a half, is currently receiving ECI services for speech delays as well. Sometimes he performs well with his therapist, and sometimes he takes lots of breaks (by running away, not cooperating, seeming agitated) because that's how he's trying to manage his stress in the session. Our speech therapist has never indicated that he might have Asperger's or any other developmental issue b/c of it. She normalizes those actions and just rolls with it in the session.
For your own piece of mind, please get a second opinion regarding the red flags. Your post doesn't indicate what sort of direction the therapists were going in terms of the "red flags", so I'm not exactly sure what issue or diagnosis they may have been leaning towards. But, if their impressions end up being on target for your child, a second assessment would at least help confirm or dispute it. It would also help you shake the "creepy" feeling you mentioned. Always trust those kinds of feelings because a mother's instincts are usually on-target.
Best wishes with this situation! Please let us know how things work out! My son will be going for his school evaluation in August.