Both are true, in a way. Battlesuits can ride on the outside of OmniVehicles with no problems, in the same manner as OmniMechs. (And suits with magclamps can ride any vehicle in the same way they can ride any 'mech.)
Suits can also ride inside any appropriately-sized cargo bay. This means that an OmniVee that has an internal bay (such as a Bolla, Badger, or whatnot) can carry suits on the inside and outside at the same time.
Whether suits can ride externally on flying vehicles, like VTOLs or WiGEs, even if said vee is an Omni, is another issue, being hashed out right now in a separate thread.
Cheers.