I find it irritating when the same people have the same embarrassed reaction often. Especially when it's things that aren't really embarrassing. Such as...
I had a chocolate bar today
I spent $50 on a sweater
I think the guy that works in the next department over is cute
I'm having a bad hair day
No I really don't find them more trustworthy. I think I'd have a problem trusting them to make any decision because it will just end with
I'm embarrassed to say it but it's true.
Anyway, I don't think I trust some people more because they're embarrassed. (In fact, I don't think I trust easily.) I'll probably have to ponder on this more and not shoot without aiming as I am prone to do.
I definitely do trust EEP (easily embarrassed people) more, and for good reason. The ease with which they slip into feelings of embarrassment means that they (1) have an active and (over) functioning superego, (2) have an acute awareness of the feelings of others, and (3) have trouble hiding their feelings. (1) is good because it means that the person is more inclined to chastise themselves when they do not adhere to their own principles or feelings about things. Even if their principles/feeling are misguided, you can trust that they will at least stick to them. Predictability makes a person more trustworthy. (2) I don't think needs explanation. (3) is good because you can more easily tell when the person is lying, which makes them easier to trust.
This is a different question from whether you like EEP or whether you find them competent.