That's the same as stating that for PADI Open Water, you need to get PADI Scuba Diver first.
No, it's an intermediate step. Once you've completed part of the OW course, you're eligible for a Scuba Diver card. But you can't skip the first part of the course.
Same with Tec Trimix. Tec65 is just an intermediate step. You can't skip it.
Tec 40/45/50 are three modules in the Tec Deep course. It is in fact one course, with 1 book covering all modules. And yes, you get 3 c-cards.
According to the PADI page I looked at today, the prerequisite for Tec Trimix is Tec 65 OR Tec 50. So you can go straight from Tec 50 to Tec Trimix. But, the prerequisite for Tec 50 is Tec 45. And the prerequisites for Tec 45 are Tec 40 AND Rescue. I'm not saying the Tec Trimix course doesn't teach you everything that's in Tec 65. I'm just saying you don't have to take Tec 65 as a separate course, ever. You DO have to take Tec 40, 45, and 50, no matter what.
As far as I (as the student/consumer) am/was concerned, the number of books is completely irrelevant. 1 book used for all doesn't make it 1 course. Nor does multiple books for the first TDI course mean it's multiple courses. We used the same textbook for Physics 1 and Physics 2 in college. Does that mean I only took 1 Physics course that year. Other classes had multiple books for one class...
If you could combine Tec 40, 45, and 50 and have a reduced number of checkout dives that covered all 3, as compared to the number required when doing them individually, then and only then might I, as a student/consumer feel like it was actually only 1 course. Also, to consider it as one course, I would need to be able to start it and continue the course on consecutive days until I finished.
If you only have the minimum number of dives required for Tec 40, I believe you actually cannot take them all together. You would have to break between courses to get more dives in somewhere along the way before doing Tec 45 and again before Tec 50. There may only be one book that covers them all, but from a consumer perspective they are simply not 1 course. On the other hand, if the instructor chooses, he or she definitely can teach TDI Intro to Tech, Advanced Nitrox, Decompression Procedures, and Helitrox all as one course. It can be done, start to finish in something like 3 days, with 6 required dives.
I'm not recommending to do it that quickly (unless your skills are already REALLY solid). I'm just making the point that it CAN be done like that, meaning it can be offered as legitimately one course. Not 3 courses done one immediately after the next.