You are correct. I've read probably 40% of those 300-whatever pages in the ADA, and re-read the sign specs multiple times to confirm things over the years, and nowhere does it restrict the background to solid colors. Now, since not being prohibited and being acceptable are two different things, and almost the entire sign section can be open to interpretation (other than sizing), but the important thing- and it's mentioned a number of times- is the contrast.The recommended contrast between letters and background is 70%.
I think that solid backgrounds are not required as long as there is sufficient contrast.
We make hundreds of these every year for local schools, hospitals and office buildings.
We are not a supplier for the sign industry at large, but one of our competitors is and they do excellent work: ASI. They are spec'd on many of the projects we bid.
https://asisignage.com/locations/kansas-city/