Cousin marriage -> defects is actually not that common. (My mother says that some random relative married a cousin and had a kid with a limb missing r”l but I won’t swear to the causality.) Sure, in some cases it may make it more likely for recessive traits to be passed on, but the risk only gets really bad after more than one generation of cousin marriage, statistically speaking.
PBA: Why is it worse if the cousin is like a sibling? Doesn’t that add somewhat of a squickiness factor to the whole idea of a married relationship? The only people I know of personally who married cousins didn’t know their spouses well before marriage (one couple, my great-grandparents, grew up in two different villages and didn’t meet until the shidduch was made). Ask the average person (well, girl, I guess, as I can’t claim to understand boys) her opinion on marrying a close cousin and the answer would probab;y be a decided “ewww.”