bullshit. I'm sure it's possible to create a modulation and encoding system that can "partially recover" a stream. if you have good signal, you get "HD quality", but with lower rates you start degrading. Unrelated, but like Wi-Fi does. 300mbit on clear view of the AP, down to 1mbit if you're unlucky.
Another thing about digital is spectral efficiency: how many bits per unit of transmission you can send. For TV with ISDB-T you can send 3 SD channels in the same space as ONE analog channel. This means, in the case of digital radio, you could use really redundant transmission. Maybe FEC with 3x the data. (FEC TLDR: it converts N packets to N + M, you only need to recover any N of those (N+M) packets, in any order, to fully recover your original data).
If you go into HAM land, they have all sorts of modulation schemes. Olivia MFSK for example, is able to receive data 10dB UNDER THE NOISE FLOOR. Olivia is able to recover information so degraded your ears can't even tell it's there. To you, it's all static.
I don't know how DAB works, but considering it was developed in the early 90s, it probably sucks. It doesn't mean "all digital sucks".
Oh and btw: ISDB-T, for example, is able to give you an excellent HD image in a situation where you'd be getting a blurry, noisy, ghosty image if you were to use analog.