I have referred to babies several times in the past as being greasy. I realize that needs explanation.
My sister read somewhere about a study they did on newborns to determine the reasons why some moms never feel like they're finished and always want another baby. Apparently babies emit some sort of pheromone- it's actually kind of like a grease, and it's addictive to adult females of all sorts, but most especially to their moms. It makes you NEED to hug and snuggle and kiss the baby because you need its grease. It's some sort of innate thing to make you want to bond with your baby and hopefully ensure it doesn't have failure to thrive, or I think that was one of the conclusions of the study. The effects of said grease taper off as the baby gets older, and disappear around age three. So, as your child hits age three, the grease wears off, you realize the terrible threes are SO MUCH WORSE than the terrible twos and why did nobody warn you, and you want another baby. Because you are going through grease withdrawals. Crazy, huh? I have no idea who "they" are or where she read about the study, but we have latched onto it because we like the concept, whether it's true or not.
So. When a baby is especially cute and delicious and we want to kiss it, we always talk about how greasy it looks. Nothing to do with hygiene or cooking oil or anything like that. :)