Ugly, incorrect color rendering isn't ever acceptable. . . . I don't expect their proprietary raw processing to match another's proprietary raw processing. That they do such a piss poor job of rendering . . .
I was using Topaz Gigapixel for quite a while before Adobe introduced its own machine-learning technique for increasing resolution. The Topaz results never struck me as entirely satisfactory, but after trying several online alternatives it seemed like the best compromise.
Not so much anymore.
I have only a limited understanding of the design of neural networks, and I'm certainly no expert on color management, but my impression is that when fed a raw file, Gigapixel emits a completely rendered image (i.e., with respect to color, output-format-referred) even when you specify a DNG container as the destination file format, while Lightroom and Photoshop produce a DNG file that is still scene-referred so you can still make color adjustments without producing artifacts.
I still use both products, but as they continue to mature—I presume both software manufacturers are continually updating the "learning sets" they use to train their neural networks—I'm experiencing less need for Gigapixel except when I need to make massive increases in resolution.
The underlying machine-learning techniques are available to everyone, so the ability to manipulate raw RGB data and produce a manipulable output file is an important differentiator. It seems reasonable that Adobe would have an edge here. I suspect that how exactly Adobe manages to preserve the user's ability to manage the colors in the output file is a trade secret. Somebody like Eric Chan could no doubt explain it, but I'm not holding my breath.