My understanding of an x-ray machine is that a high voltage is applied between a cathode and an anode. The cathode is a thin tungsten filament--not unlike a lightbulb filament. As it is heated it ejects electrons which are then accelerated by a very high potential, usually around 50kV, between the cathode and a rotating anode, also made of tungsten. X-rays are produced by the energetic electrons slamming into the tungsten atoms at the surface of the anode, which causes many of the anodes surface atoms to lose electrons. The process of these charged atoms moving with the rotating surface emits most of the energetic x-rays in a process called Bremsstrahlung radiation (which is related to the movement of charged particles through a magnetic field.) The rest is generated when the atoms neutralize themselves again.
As such, the x-rays are generated because of electrons interacting with the deep shells of electrons within the tungsten atoms, and do not have anything at all to do with the nucleii. As such, this is a non-nuclear process.
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However, having just said all of that, it is possible that certain x-ray machines may use a very small amount (microcuries' level) of radioactive isotopes, such as Polonium-210, or Americium-241 to dope the tungsten cathode filament. Such a doping with a very small amount of radioactive material would cencievably boost the electron emmission efficiency of the tube, and thus would increase the x-ray yield for a given power llevel. I've heard of this being done for certain RF-power amplifiers which are vacuum tubes of a different sort, so it is conceivable that this is done in x-ray tubes as well.
Still, x-rays are essentially an electronic phenomena (having to do with the inner electron shells of high-Z materials) and gamma rays are almost exclusively nuclear phenomena having to due with energetic transitions in the nucleons in the nucleus of the atom and having nothing to do with the electrons orbiting outside. The only places where the two could overlap in a non-nuclear way woud be in energetic particle accelerators, and concievably very near the surface of a neutron star with a powerful magentic field. Only there is it conceivable that Bremsstrahlung radiation could be powerful enough to directly generate electromagnetic radiation with wavelengths shorter than x-rays. Indeed, it is concievable that gamma-radiation is more or less just Bremsstrahlung operating at the conditions that exist within a nucleon--which could be similar to the conditions near the surface of a neutron star.
I quote from you source the sentence where I found radioactive sources mentionned:
If the x-ray device contains a radioactive source, replacement, leak testing, or other maintenance or repair procedures shall be conducted only by individuals specifically authorized under the University’s Radioactive Materials License.
And from this, you deduce that X-Rays are produced by radioactive sources? I would rather deduce that some X-Ray machines contain a radioactive source, which is really not the same. In fact, X-Rays are generated through bremsstrahlung by accelerating electrons into X-Ray tubes, and not via nuclear decay.
Now, why do I insist even if I have said it was a pointless debate? Just to show you everyone can do mistakes, even you.
In fact, even on Earth, it is possible to produce bremsstrahlung radiation of very high energies (up to 1 GeV!) with high-emergy particle accelerators. Look at the site below:
I believe you are correct in using the word "some" x-ray machines don't use radioactive materials, with the quote you found. My x-ray machine fits the standard housing of it's radiation source, also fitting this discription fom the source I quoted...