Here in the following sentences why are we using "I thought she might have had" with 'had', why not simply "I thought she might have"?
1) Vincent remembered Eddie’s wife, “I knew Naedine very well; she was very nice to me. I felt I had a great rapport with her".
Vincent said, “Eddie didn’t talk much about it, but I thought she might have had a problem with alcohol. One New Year’s Eve I caught on right away. We were at the Inn at Jefferson Square. I was sitting at the table with my date, some friends and Naedine. She took a glass of wine and Eddie came over and told her she wasn’t supposed to be drinking."
2) “I thought she had a good chance to get on the medal stand,” Dunn said Monday. “And if she got a good jump, I thought she might have had a chance to win it. That one girl just got an amazing jump in. Tanae jumped better than she had ever jumped in her life. You can’t do much better than that. When you jump the best you’ve ever jumped at the state meet, that’s all you can ask for.”
In both of the sentences above why can't we say "....might have..." like here:
The big woman's face was bright red. For a minute I thought she might have a stroke. It was 100 degrees in the shade. (Ref)
Although I know about tenses (past tense and past perfect), this seems to always confuse me. Also it is always very easy to understand without 'thought' but with 'thought' it looks confusing.
Please elaborate this point.