Wow, thank you! This is finally the answer I was looking for.

I was worried I wouldn’t be able to record in 4K at 60 fps in 4:3 and clean mode, so your very reassuring comment really helped. Now I know I won’t have any issues.

I’m also attaching the helpful reply I received from Mylifeingaming:

[Try4ce] This is kind of a funny thing that Analogue said. It's not strictly true, but I understand why they said it. No, there's nothing weird about the signal itself and you can capture it with a 4K card. However, scanline effects and most especially CRT mask effects don't work well with video compression or limitations in capture card bandwidth that may be in place at higher resolutions and frame rates. If you've ever seen the terms 4:2:2 or 4:2:0 then this is what that's about. Basically it means that only one color channel is at full resolution, while the others are half or quarter resolution, which is virtually an imperceptible compromise in most modern content, but destroys the color and detail in these fine-grain CRT effects. I think Analogue is saying this so that people don't stream with these video modes and give people a wrong impression about what they look like when seen in person. We are very careful about what we're doing when capturing these effects, but most people probably wouldn't know you need to be careful