DD is 3 and we EC'd, she's been a 'graduate' for ages now. But we still SOMETIMES remind her, and she even SOMETIMES still has accidents. It doesn't mean they're not "trained", it just means they're still very young people who sometimes goof up.
MOST of the time, we just let her go about her business and she goes by herself. Runs to the bathroom, wipes her own bum, the whole shebang.
Sometimes, if she's really engrossed in an activity and we see her 'dancing' and holding herself, I'll ask her if she has to go pee. Most of the time, she'll say "NO", but 5 minutes later she says ".... I gotta go pee" and runs off. So I don't press the issue once I've mentioned it -- maybe a reminder that she "probably doesn't want to pee in her pants, right?" then I leave it to her.
Or if we're going out somewhere for a long drive and she's being belligerent about it, I may lay down the law and make her try. USUALLY she eventually sighs and cooperates, because she's a good kid like that heh. (The sigh is soooo funny, she gets it right from me). If she really resists, though, I stop pressing. Odds are she really doesn't have to go. And in the last 2+ years, we've had a total of ONE pee in the car seat, and ONE pee on the sidewalk in front of the store. That's it.
One thing I learned through EC'ing from a very early age, is that she can often go a LONG LONG TIME between pees. I'm scratching my head thinking "SURELY she has to go by now", and if I'd had her in diapers all along (and thus less aware of exactly she was peeing -- and she less likely to 'hold it' for any length of time in the first place) I'd probably be "bugging" her every couple hours to go pee. I expect the same is true for most kids once they're "conventionally" trained too -- just because they haven't peed in a distressingly long time doesn't mean we need to press them to go!
So I concur with the advice you received, and which you've followed -- and just lay off almost completely. Reserve the reminders for when they're truly needed -- when you recognize that an accident is about to happen, when you're going out, etc. If they're only occasional, he's more likely to appreciate them rather than resist them. Then if things go really messily wrong, you can re-evaluate your tactics.
But don't worry too much if there are some messy days, either. Without you 'reminding' him all the time, he has to learn how far he can "push" his holding it. And sometimes they learn that lesson the hard way... "Oh, THAT's what it feels like when I really can't hold it any longer..." Heh. Once he's experienced that a few times, he'll likely go back to being 'clean'. It's all part of the learning process.
Sooooooo much less stress for both of us, and guess what? No accidents. I pretty much knew that he wouldn't have any, but just felt like I needed to keep reminding him.
Ah the joys of potty training. 
