Hmmm, I see what you mean. It's not totally clear whether it's just the bride who's of the named parish, or both bride and groom, but it's interesting that where a parish is named, there is no third person mentioned. It also seems unusual that it would be the bride who was marrying away from her home parish, as opposed to the groom.
I've seen a lot of early marriage registers but never anything like this, so I'm as curious about it as you are now. The bondsman idea is a theory, at any rate, but not one I'm 100% confident in.