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"Es posible que estuviera durmiendo" and "es posible que haya estado durmiendo" doesn't convey the same information, including nuance. You just described people who is not aware of that and yet they have an opinion.
"No sé, es posible que estuviera durmiendo pero es más probable que haya estado despierto."
Try to swap both tenses and see what happens:
"No sé, es posible que haya estado durmiendo pero es más probable que estuviera despierto"
A keen native speaker can imagine completely different contexts for both phrases. For instance, the first sentence suggests all could happen in a certain point in the past. The second one suggests an ongoing process in the past. It has to do with imperfect and perfective aspects.
A piece of advice: don't ask native speakers about what is correct about subjunctive or why some case of subjunctive appears unless they have a)an education on that specific subject, or b)they have experience, like many in this and other language forums, in analysing their own language without falling in the catch of hidden imaginary contexts. And even with a) or b), take everything with a pinch of salt.
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