That’s a really good question! So I googled the two restaurants you mentioned, and they definitely look a bit more elevated than your typical hawker stall. That said, they don’t look like they’re served on a plate of straight soy sauce, but rather a soy-based (with garlic?) broth, similar to what gets poured over boiled gai lan at dim sum.
I don’t know which hawker stalls you went to, but my experience was that the basic plate of HCR was dry with 3 dipping sauces on the side, sometimes a bowl of chicken broth also on the side. Chicken and rice plated together or separately.
As I said above, the combo plate I ordered at Ah-Tai included some veg (gai lan), but that was an add-on. Otherwise mine (below) would have been sans broth and as pictured above.
Edit: so I got curious and yelped some pictures of Ah-Tai, and now I’m a little more confused. The majority of their pictures seem to show the dry preparation I tend to think of, while some definitely have more of a wet presentation. Further muddying the waters is that I’m seeing different platings of ostensibly the same set I ordered, some with the chicken on top of the veg like mine, and others with the components plated separately and the chicken dry.
I’m not going to pretend to have an answer here; I’m going to ask my friends and get back to you all