That is true. However, most of the Tritium produced in the DD reaction would be burned off before leaving the reactor. This means that the advanced Tritium handling facilities of JET, for example are not required. This does make it 'cleaner' in a way, and means that the tritium is not 'involved' in the reaction per se - it kinda... appears in the reaction and most of it goes away afterwards. I think this is what is being implied here - no tritium is needed to start the reaction, nor are the handling facilities needed.
DD is much cheaper than a DT reaction. However, DT is better for power production, and commercial fusion reactors will probably use the DT fuel mix. ITER will be running DT, and JET set its record with a DT mix, and will probably run more DT experiments in the future. Most reactors run DD however, because of its cost advantages, it's a little cleaner due to the lack of tritium handling required, and is useful for simulations.