i think this is what they were thinking of when they said that, because tritium is not a byproduct of fission reactions. fission produces heavy elements. the only possible source of tritium would be absolutely miniscule amounts of hydrogen in the moderator getting activated (twice). and mind you, we're talking not enough to even find here.
Fission products are always lighter than the fissile material. A nucleus of the atom can go through a number of fission reactions, and the end results are not always the same.
However, neutron bombardment typically
activates elements, which means the stable isotopes can become unstable isotopes, which means radioactivity. And the neutron bombarded nuclei can react in a number of ways depending on bounding energy of the nucleus, bounding energy with the new neutron introduced, energy of the neutron and so forth. Slow and fast neutrons react in a different way.
For example, in a typical fission chain reaction, Uranium-235 is impacted by a neutron, which can have two end results: Neutron absorption to Uranium-236 which, if it stays as such, is a bloody nuisance, or in a very short-lived U-236 nucleus that promptly decays through fission into daughter nuclei (fission products) and additional neutrons which will initiate new fission reactions. There is no way to know what the fission byproducts of a single reaction will be, but in a larger mass, the proportions of fission products can be predicted with significant accuracy and precision. U-235 mostly fissures into iodine, cesium, strontium, xenon and barium, and these radioactive isotopes start decaying immediately, which causes the radioactivity of nuclear waste. Usually, the fission results in two nuclei of relatively same atomic number, but sometimes one of the daughter nuclei happens to be tritium - about one in ten thousand reactions results in tritium, and other light elements/isotopes have similar yield rates. This is enough that the tritium accumulated in used fuel rods can be worth extracting.
There are also fission reactors specifically built for production of tritium, seeing how it is a valuable element for scientific and military applications alike.
Production of tritium directly in a fusion reactor still requires a "start-up" amount of tritium in the reactor each time the reactor is ignited. While the reaction goes on, neutron flux will impact the lithium-coated walls/floor of the reactor chamber, and tritium nuclei are produced. Problem, then, would be to induce those nuclei into the plasma where fusion is ongoing. If that works out, then you need to figure out if the production of tritium can be equal or larger than the consumption of tritium, which will decide whether it's possible to sustain the reaction with lithium-originating tritium once it gets going.
Of course, helium-3 would be a much less problematic fusion fuel combined with deuterium, since that sort of reactor would have predominantly no neutron flux at all - it would produce Helium nuclei and protons. The reason why neutron flux is annoying is because it makes the reactor itself radioactive via neutron activation as explained before - and that means that even though the reaction products are harmless and even useful, the parts of the reactor will become a problem, their service time will be shortened because radioactive decay changes the structural properties of alloys, and the reactor as a whole becomes a total ***** to service because it becomes a radioactive environment. It won't be anywhere near the amount of radioactive waste produced by fission power plants, but it'll be a problem nevertheless, as long as the fission reaction itself produces a strong neutron flux.
So, the solution? We need to figure out an abundant and reliable source of Helium-3.
Which means, hopefully, that we'll eventually go and start mining the Moon and the asteroids. In which case it would be a win-win scenario...
EDIT: of course, tritium naturally decays into helium-3, an electron and electron's antineutrino... so if we can get production of tritium to high enough levels, that would mean it would also be a source of He-3.
But that would mean no reason to become a Moon Miner...
sadface