I’m not an expert either, but I can read. The Uranium ore which was stored in the buckets is typically something like 99% Uranium-238 (U-238 or 238U) which is common in nature. The ore is radioactive, but the type of radiation is significant.

I found the following section of the U-238 page interesting because it describes how U-238 is used for shielding. From that description, it’s fairly easy to discern that Uranium ore emits Alpha radiation (which was probably absorbed by the plastic buckets), but would not be a source of Gamma radiation as U-238 is used as shielding from Gamma radiation.
Quote:
Radiation shielding
238U is also used as a radiation shield – its alpha radiation is easily stopped by the non-radioactive casing of the shielding and the uranium's high atomic weight and high number of electrons are highly effective in absorbing gamma rays and x-rays. It is not as effective as ordinary water for stopping fast neutrons. Both metallic depleted uranium and depleted uranium dioxide are used for radiation shielding. Uranium is about five times better as a gamma ray shield than lead, so a shield with the same effectiveness can be packed into a thinner layer.


Grand Canyon tourists exposed to radiation, safety manager says
Quote:
“The report indicated radiation levels at "13.9 mR/hr" where the buckets were stored, and "800 mR/hr" on contact with the ore. Just 5 feet from the buckets, there was a zero reading.”
Scary if you don’t ask, milli-roentgen’s of what?

What does it all mean? I for one wouldn’t be concerned about the ore itself. I would be concerned about going public before all the facts and exposure data are in, possibly needlessly causing a scare. OTOH, why store multiple buckets of Uranium ore in a museum where some toddler could stick something in his mouth? That was just dumb.

Again, I’m not an expert on Uranium radiation, but this seems to be hype to make a point about a “cover-up”; sometimes you really don’t want to watch sausage being made.