Ok honestly I doubt it matters much.
There is plenty of history behind horizontal storage with the belgian sour styles.
Most American corked bottles say to store upright.
Wine by comparison is still, and stored horizontal to keep corks moist and prevent cork rot as they dry out from upright storage. I doubt the corks would lose elasticity as long as the proper humidity level is also observed. I doubt co2 would alter that I the setting of beer stored horizontally.
I've not gone and searched for any pure scientific experiments, research, etc on the subject though.
I have a fridge I store mine in upright, and a few in the drawers on the sides, as well as a wine fridge with shelves on which I also store beer, some corked, some capped, horizontally. Can't find any negative attributes when stored on side so far,
TD