I don't recall seeing this stated explicitly, though it probably is. It's a pretty straightforward deduction from what's known about HPTA feedback. Estrogen and androgen receptors in the hypothalamus and pituitary respond to free testosterone and its free metabolites to regulate testosterone production. There's additional regulation at the hypothalamus—For example, calorie deprivation reduces testosterone production; sex becomes a lower priority when there's not enough food.

To reiterate: The body is not measuring and manipulating total testosterone. The body increases or decreases the production rate of testosterone to attain the desired level of free testosterone. SHBG does not have much effect on free testosterone, so its regulation is not intended for that, as opposed to it's buffering ability and other independent functions. We know that androgens tend to reduce SHBG while estrogens tend to increase it. T3 increases it. Albumin, as a general transporter protein, is even more independent.