I think the term "oily nails" has been taken to literally both from techs and clients.
The term puts images in minds that the nails themselves are producing oil, hence oily nails but as already stated, the nail can not product oil as it has no sebaceous glands.
I do think what it means though is exactly what again has already been mentioned, grot and grime from outside sources sitting on the nail and making it appear oily and of course the cuticle as it grows out along with the nail.
So yes, a thorough prep is indeed needed to ensure a clean surface and this should include a dehydrator to balance out the Ph of the nail surface ready for application of primer (if the system has a primer) and product.
It should also include a cuticle remover and cleanser too.
To many techs just remove shine with a file and think this is all the prep they need to do and then when the enhancements don't last, they use the excuse of "oh, you have oily nails" instead of taking a good look at themselves and if they are doing a thorough job.