If you can send the drain down through the floor to a lower level P trap, you can do that. My saying this is not a recommendation "per se" in and of itself, it is just information, which may need further caveats.

If the P trap for this DW is in the kitchen, you need to install a high loop.

If you know what a high loop is, install that.

High loop means to raise a portion of the dishwasher's flexible drain line as high as you can under the sink (e.g. with a piece of bailing wire). This will prevent contaminated water from backing into your dishwasher, unless the backup goes right up to the rim of your sink, in which case, an above-sink air-gap is the only thing that will prevent cross-contamination.

The DW drain line branches into the sink drain line below the sink -- regardless of what type your faucet is. I suspect you have a contractor who I would consider a case of borderline fraud.

Your contractor must know what a high loop is. He also must know that any dishwasher drain connecting to the kitchen P trap goes first through a high loop or an air gap.

In both cases (high loop and air gap), the drain plumbing connection has no relationship to the faucet you chose to install. That is supply plumbing not waste plumbing. Perhaps I have misunderstood your post or you have misunderstood what you thought he said, or some other explanation is possible, et cetera. If not, you have a special case of a contractor saying that the faucet prevented him from raising the dishwasher hose in a high loop and thereby routing its waste water up first before it goes down into the P-trap and the house drain.

HTH

David

Sorry, I wrote too fast above. A single-drain sink (the Orca in this case) needs a Dishwasher Wye or a Dishwasher Tee connected to its drain prior to the P trap. This is normal and common. There are millions of them installed with dishwashers next to them and draining into the sink drain. Perhaps your contractor never looked at a single drain sink before with a dishwasher next to it.

David

Agreeing with David and rephrasing what he had to say, what your contractor says makes no sense and might make you wonder whether you should be looking for a new contractor. With an airgap your dishwasher would be connected to your drain via the airgap. Without an airgap the dishwasher would be connected to your drain via a high loop. In either case, as David also said, you'd need a wye or tee connected to the sink drain - in other words, no difference with/without an airgap. My guess is you've misunderstood the contractor because otherwise it's hard to imagine a contractor that incompetent. Another possibility is that he's saying that local code doesn't allow him install without an airgap, which would not be unusual. In other words, he knows how to install without an airgap but isn't willing to. In an identical situation, we put in the additional hole, then replaced the airgap with a high loop and the airgap with a soap dispenser, which is at least useful.

Thanks for the help. I gave him this info and we had it installed right after Christmas!