It wasn't that long ago that I commented on mamasource that I was discouraged by my son's inability to catch on to the whole potty training thing. He had no interest at the age of three, so we waited a little bit. We put him in pull-ups a little after age 3 but it was nothing for him to do his business in his pull-up. We put him in big boy underpants after his teacher in preschool said he was going all day with no accidents, which was when he was a little over 3 1/2. He turned 4 this past November and still was pooping, and occasionally peeing, in his pants. And, like your son, he too had no problem with wet or messy underwear.
At his 4 year check-up, I asked the doctor about it and he said to not force it, especially the pooping part. He said it's sometimes "a deep seeded issue" for some kids and when you try to force it, the child can try to hold it in causing impactions which can be very bad.
My husband and I tried very hard to be patient, keeping him in big boy underpants and changing poopy ones on a daily basis. A couple times, we caught him right before he was going to poop and got him to go to the potty on time. Then, one day, he just started going by himself. It's like all of a sudden, he could tell when he needed to pee and poop and we didn't even have to remind him anymore. We did have "big" rewards (2 different Lightening McQueen matchbox type cars) for the first 2 times he pooped on his own, and then m&ms for each time after that for about a week or so. After that, he would go on his own with no prodding from us and I think he's had maybe one accident since then and that's it.
The thing you need to know is that all children are different. My daughter trained well before she was 3 and only had a few accidents before she was fully trained. My nephew turned 3 at the end of this past November and he's already fully potty trained. That's almost a year earlier for him then for my son.
I know what you mean about the "stigma". My aunt and cousins would question why my son wasn't trained already when they came to visit us when my son was about 32 months old. And I could hear the gloating in my SIL's tone when she would talk about how my nephew was almost fully trained and he's a year younger than my son. My son wasn't even interested until most kids are already trained! But I'm here to tell you my friend, when it clicks, it clicks. Just be patient and encouraging. They will do it in their own time.
Good luck! :-)