Dishwasher Fill Line from Under Floor?

I've been working on installing a dishwasher into a house that has never had one as we're preparing the house for sale, in between a dozen other projects. Finishing the install and replumbing the new sink is all I have left. Because we're moving, I have about fifteen hours to DIY, then I'll have to capitulate, pay someone and suffer my family's teasing.

The dishwasher is a long ways from the sink and when I had the drain line, fill line and cord running through the same hole, it made the stove sit too far from the wall because its frame bumped all of that as it run behind. Now I need to expand the cabinet holes to be up against the wall, if not a little recessed and it occurs to me that it might be better to send the fill line through a hole of its own. It'd be even cleaner, if I could send the fill line though a hole in the floor and run them along the basement rafters to the sink. Of course it'd also be great if the drain line could follow the same path, coming to a drain loop 32" from the floor, under the sink, but I've read a lot on this and other forums that say the drain line must say above the floor instead of going below, but I've seen nothing to say that's inadvisable for a fill or supply line.

Can a fill line run under the floor? Any thoughts?
There will be no inspections. Permits aren't required.

Thanks

 

No problem whatever with bringing the fill in from below. It's done all the time.

 

Agreed. All my water supply lines originate from the basement.

 

You don't have to run from sink if you have a closer place to tap into. Just be sure to include a shut off valve.