Yea, that happens with all cabinets below the kitchen sink if you are splashing water there all the time. We also see it in bathrooms below that sink, and it really happens with high quality cabinets too, not just the cheap ones. As for painting them, you do not really need to strip away the old finish...you just want to dull the sheen to help the primer adhere as best as it can. We always hear these stories about people that are skipping the sanding or skipping the primer and everything is holding up fine, but in my mind, this doesn't mean we should discard what we know works just because a few people claim to have great results. Some paint manufacturers are even claiming that you do not need to prime at all and that their paint will stick to anything, but I'm aware that everyone lies in their marketing materials these days because all they care about is selling product, so I'm sticking with my tried and true methods that I'm positive will work and you will hear the same tune from all professionals. If your cabinets are not real wood though, I would be fine with a high quality acrylic primer, so perhaps you do not have to use oil.

Paintguy...thank you for your making-all-sense reply :-) very informative..

Those cabinets will paint VERY NICELY if you follow paintguy's instructions - clean, sand to knock down the gloss, good primer, and good paint.