Actually TPI makes a tire more supple or flexible because the threads are thinner. More, thinner threads are more flexible than fewer, thicker threads even when the total weight of the threads is the same in each case. As far as the ratio of rubber to fiber, I don't know whether that varies with TPI or not. My guess would be not necessarily, although these days high thread count is pretty much reserved for the tires which are "best" in many respects, so they are designed to weigh less than tires with low thread count. Since they are intended for smoother roads and special "race" days, they likely do start with less rubber.

In case anyone is interested, the reason more, thinner fibers are more flexible than fewer, thicker fibers is the same as the reason a small diameter cylinder (frame tube) is more flexible than a large diameter cylinder of the same weight. Stiffness depends upon the third power of the radius of a rod or cylinder (of a given length and material), while weight only depends upon the second power. So at equal weight, the larger radius member is stiffer.