Because the radiation is sent in a burst, [..] the DNA
damage may be far greater than a similar dose of cosmic
radiation.
People keep repeating that, but it is not simply true. DNA can get damaged when a single photon excites an electron and consequently influences the molecular structure. The chances of multiple photons operating on the same electron at the same time, even in cases of a radiation burst, are negligible. The person is affected by the same number of photons, which results in the same number of chances of electrons being excited. The number of excited electrons will be equal and the resulting damage will be equal.
Now it may matter that the damage is more localized in both space and time, but no one has shown this. Firstly space: spreading the radiation over only the surface, for instance 1/10th of the body (remember that surface times a small depth is always a relatively large part of a volume), means 10 times as much damage. But if the average amount of damage in the skin was one broken bond per 1000 cells, it will now be one broken bond per 100 cells. As the repair takes place per cell, that doesn't change anything for the total chances to get cancer. Only if the amount of damage in a single cell, and close enough to each other to be relevant, changes, then this type of operation may pose a problem.
Secondly for time: everything depends on the amount of time it takes a cell to repair DNA damage. If the average time of repair takes 3 seconds, then during a flight, some damage will be repaired before other damage takes place. The backscatter machine delivers its dose faster and damage may accumulate. However, if repair takes 30 minutes on average, the difference is again neglible.
The point is not that I know the numbers: the point is that people making claims don't know them. They are just claiming things that seem to make sense to them, when they draw an analogy with a car crash or something. They don't understand what is actually involved.