I wonder if the grease is indeed washed away. Some of it may be hydrolysed through the alkalinity of the developer, but I would think that it will at least leave a mark, if the fingerprint is on the emulsion side. It's grease, and grease repels water. Make a fingerprint in a glass and pour in some developer for a while. Then empty the glass and see if the print is gone. I guess it will at least delay the action of the water-based developer until it has been hydrolysed.(posted 8992 days ago)I don't think there is much to worry at this stage about finger prints on the back of the film.
If you find it necessary to "sandwich" the film between finger and thumb (as Shawn so neatly put it) there might be something wrong with your tank/reels, or at least with your technique. The film should be eased into the reels, being guided at the edges. Avoid holding the film too tight as sharp bends may lead to blackening of the emulsion and to opaque spots in the film base.