I know a lot of lacto-ovo vegetarians consume honey, but I've never heard somebody claiming to be a vegan say they eat it. Bees are animals - therefore honey is an animal product, and you can't consider yourself vegan if you use any animal products.
Some people may not care if bees are enslaved, manipulated, killed (beekeepers often kill off their bees before winter, and kill the Queen before she is due to die to keep control of the hive), and the honey they work hard to produce stole - after all, they're insects, right? Not real animals. Not as important as cows or chickens. This is the same line of reasoning omnivores use when distinguishing pets from livestock. But there is some research suggesting bees are intelligent, which I'm sure you can find if you Google it, and that they are very capable of feeling pain.
Besides - honey doesn't taste that great and isn't a part of many products, so it's not hard to cut it out. The idea of eating bees regurgitation disgusts me, anyway.
I guess those people have the notion stating that bee honey are made from pollen grains which is slightly correct. Honey is the product of bee and bee is an insect, an animal, and as stated by Lion , eating animal products would make us not vegan. Those people don't know yet the full idea of being a vegan. That is why they told you that they are Vegan, but still they broke the law of being a vegan.
Some people think that bees are somehow different to other animals, or that honey is "just a by-product" or that for some other reasons it should be permissible to consume honey and still claim to be vegan.
I do not agree with these views, and I find that honey is one of the easier things to avoid...
I think many people don't consider bees animals. They're just bugs, gross, they aren't animals or sentient. I find honey the easiest thing to avoid as well.
There is also many who are not vegan for ethical reasons, so the bees just don't factor in. Honey is considered healthy, so they have no reason to cut it out of their diet and it makes the whole sweetening process that much easier for those on a plant based diet.
Bees work so hard for us.. living, breathing things.. no thank you.