Out and out lie.
That statement does seem hard to support given years of research on the effectiveness of masks against viral infections, and the current rates of COVID-19 spreading among populations of people wearing masks.
The CDC article that ABC news links to itself cites a study from Thailand. Interestingly that study finds that staying just 1 meter, or three feet from the infected person is more effective than wearing a mask. But somehow that result got ignored when the results of the study were written up.
Here is the original study that the 70% claim cites to. Note that the odds ratios are lower for 1 meter separation than wearing a mask.
I think a lot of the CDC publications at this point are really just PR pieces, not actual scientific studies.
As you noted it is really unlikely that wearing a simple cloth face mask reduces the infection risk by 70%.