If you use one of the newer predictive voice codecs, expect a lot less success, but maybe moving to older/slower modem speeds will help.
V.34 was mostly a speed improvement, as far as I remember, no?
https://en.wikipedia.org/wiki/T.38
edit: That is I assume that they meant VoIP when they say digital phone lines. Fax over digital ISDN lines has been reliable since its inception as far as I am aware.
You are right btw. I was working off long disused recollections and then had to leave.
Faxes routinely get 9600 and 14,400 speeds over these ATAs; it helps a great deal if your coded is G711 which is an uncompressed codec (it is u-law PCM in the USA; PCM is just like the bits recorded on a music CD, but at a much lower bitrate).