Radiation levels were reported (at the high end) as being 30 times greater than background levels. They were in the plume for five hours. That would be equivalent to (30 x 5 hours) or 150 hours, or 6.25 days of normal exposure.
It isn't credible that the small amount of extra exposure would result in numerous cancers.
If we know the mix of isotopes in the plume, we could consider what cancers are represented. Iodine 131 is a prime candidate for thyroid cancers, for example. But thyroid cancers are not mentioned.
If you believe the Navy is lying, (yes governments do lie) what is the motivation? Here is a summation of the Navy's response from the source you linked to:
“The DARWG’s report on radiation exposure received by Fleet-based individuals, which was peer reviewed by a non-governmental council of subject matter experts, determined that the highest whole body dose to any U.S. fleet-based personnel during Operation Tomodachi is much lower than levels of radiation exposure associated with the occurrence of short or long-term health effects. For perspective, the worst-case radiation exposure for any U.S. fleet-based personnel during Operation Tomodachi is less than 25% of the average annual radiation exposure to a member of the U.S. public from natural sources of background radiation, such as the sun, rocks, and soil.”
This happened during the Obama regime, hardly a friend of the U.S. military, and hardly one to worry about spending a few more million when it has been borrowing trillions.
Why wouldn't President Obama wish to discredit the Navy and put the U.S. a bid deeper into debt?