I have to admit, it's a bit hard to reconcile the Valiant with the NX-01, which in "Broken Bow", was strongly indicated to be Earth's first deep space exploration vessel.
Then again, it's also hard to reconcile how this ship, which was almost certainly cruising along at something less than warp 2 could've reached the galaxy's edge.
Come to think of it, it's been a while since I saw "Where No Man...": Did they explicitly say the Valiant was an Earth
ship? I'm sure they probably did, but it would at least give some leeway if they hadn't.