While this clearly is marketing BS there is a certain truth to it. It depends how you define "fast". DAB has a higher bandwidth, so can transfer more data more quickly than a lower bandwidth analogue FM, transferring the same amount of data more quickly is arguably a reasonable definition of the word fast.
It would be fair to say that DAB has a higher bitrate and can therefore receive better quality audio. This irrespective of the fact that most radios don't claim to be hifi's, and that most hifi's do not offer high fidelity reproduction of the signal input these days, and that a goodly number of DAB radios are in cars with such high ambient noise from the road that any sound improvement is drowned out and unnoticeable. That one can accept as normal marketing bullshit.
But it's still not faster; both play a 3 minute bit of music in 3 minutes. Arguably, DAB is slower because it takes time to buffer etc from the start of a transmission.