Rebar sitting on the dirt - is that right?

Concrete cast against soil needs a good chunk of cover under the bars, typically around three inches, so bars sitting right on the dirt is not great. If they pour and the bars stay down, you end up with barely any concrete under them, and that's where moisture wicks in and rust starts. Rusting steel also expands and can pop the concrete over time, so your instinct isn't wrong. That said, the 'we'll pull it up as we pour' thing is a real technique, not total nonsense. It's called hooking the steel. One guy rakes and lifts the bars while the concrete flows in and the vibration settles everythign. On a small footing with a couple of guys who know what they're doing, it usally works. But it depends entirely on them actually doing it, and it's easy to get distracted with a truck timing out and end up with steel half buried in mud at the bottom of the pour.

The better way, and what I'd ask for before the truck shows up, is to have them set the bars on something. Half bricks, chunks of broken concrete, or proper plastic chairs all work fine. Takes five minutes. Then nobody has to remember to lift anything mid-pour and the bars stay put even if guys walk through the trench.

One thing to know though: in a strip footing you actually don't want the bars dead center like you would in a slab. The footing bends downward under load, so the tension is at the bottom, and the steel belongs in the lower third. Low is correct. Just not touching the dirt low. So I'd have a quick word with the lead guy, not the laborer. Say you want the bars on spacers with a few inches of concrete beneath them. Any decent contractor will just say sure and do it. If he pushes back hard on that, that tells you something too.

On my garage footing last spring I put a flat stone under every other bar before the truck came, took maybe ten minutes with two of us. When the pour was done I probed a few spots with a thin rod and the steel stayed put, no sagging. The 'we'll lift it as we go' line only works if there's acutally someone assigned to it, and on a busy pour that person is usually the first thing to get forgotten. If I were you I'd take a photo of the trench right before they pour too, just so there's a record of what went in the ground.

One thing I'd add, if this is permitted work, your inspector will look at exactly this before sign-off. Mine made the crew re-drape the steel on a footing once because it was sitting in the mud. Costs the contractor time and they know it, so that's leverage you don't have to feel awkward about. Also snap a few photos of the trench now, before the pour. If anything cracks or settles down the road you'll want proof of what was down there. Cheapest insurance you'll ever get.

Update: talked to the foreman this morning and mentioned the inspection angle, and his attitude changed fast. They're putting down some offcuts to hold the bars up before the truck comes. One thing I'm still fuzzy on though, after it's poured, how do you actually confirm the steel stayed where it should? Is a rod poked down at the edge enough, or am I overthinking it?