I had a similar experience recently, the dental assistant told me "we're going to do your x-rays now, but the controller isn't working right so I have to use a workaround, it'll take a little longer." I told her to stop what she was doing, there would be no x-rays for me, and explained why. I'm 99.99% certain I would have been fine, but the Therac-25 story is so horrifying, I decided to give in to my irrational fear.
I am a medical physicist. The Therac-25 disaster is retold and explained to every student of medical physics, of course. So I'm happy to inform you that it is not physically possible for the kind of error that occurred with the Therac-25 to occur with a diagnostic X-ray system.
You see, there are basically two kinds of X-ray machines used in medicine. One is just a standard cathode-ray tube (in fact, CRT televisions are basically the same design and both fall under 21 CFR 1020): a very high voltage is produced between a hot filament cathode and a tungsten anode, and electrons leave the cathode [1] and fly towards the anode where they produce X-rays. Because the energy that accelerates the electrons is entirely contained in the electric field between the cathode and the anode, the electrons cannot reach the required kinetic energy without moving towards the anode. All diagnostic X-ray imaging equipment is basically of this form, although there are a few unreliable machines that come with fancy sales pitches where the hot filament is replaced by some carbon nanotube thing. Nobody recommends these, but they aren't dangerous either.
The other kind of X-ray generator is an accelerator. Here there is also a cathode and an anode, but in between there are additional electric fields which take the form of standing radio waves. The released electrons are synchronized with the radio waves so that they gain far more kinetic energy from the oscillating fields than they do from the static field between the anode and the cathode.
In an accelerator, it is possible for the electrons to fly past the anode and hit the patient directly. This is what happened with the Therac-25. Only about one percent of the electron energy is converted into useful X-rays when fast-moving electrons strike a piece of tungsten (or any other material; tungsten is the most durable).
In some cases, you actually want the electrons to hit the patient. This is called "electron-beam therapy" and it is used to treat skin cancers and other shallow tumors because electrons do not penetrate as deeply as X-rays. In order to do this safely, the electron beam intensity is reduced dramatically, to about 1% (of course) of the "tube current" used to generate X-rays.
You may have already guessed the problem. In the Therac-25, it was possible for the electron beam to be configured at an X-ray intensity while the beam-directing magnets (we say "bending magnets") were aiming it at the patient. This causes a lethal overdose of radiation — a hundred times too much.
However, a diagnostic X-ray tube does not have any magnets directing the beam, nor does it have any standing radio waves ("RF oscillators") accelerating the electrons enough to escape the potential well created by the anode. These machines cannot produce electron beams outside the tube because the electrons are simply "falling" into the anode and there is nothing to "push" them away. It would be a little bit like dropping a rock down a well and seeing it fly back up into the sky.
On the other hand, dental x-rays are overused and do not improve dentists' ability to detect cavities in most patient populations.
And even though a diagnostic x-ray machine can't point an electron beam at you, it can still give you a bigger than intended dose. (Yes, I know that dental x-ray doses are typically very low to start with).
