Taking anti-inflammatory supplements increases SHBG. In fact, more than 2 cups of green tea per day will do it.
They took my SHBG over 90!
It's important to note that this is not true for all men. I drink anywhere from 3 to 9 cups of green tea per day (over 7g quality raw leaf.) Zero increase in SHBG. Zero as in zero-zero and not even slight.
If the anti-inflammatory supplement advice were true, all of the high anti-inflammatory supplement takers (say, a majority of the hair loss treament community & the entire anti-aging community as a whole) would see SHBG elevations, and yet they do not.
As far as green tea studies that track SHBG, most are done in Japan and in women that are post-menopausal or that have PCOS. In these studies, the SHBG increase tops out at 1%. For an average 30 nmol/L guy that'd boost him all the way up to... still 30 nmol/L, when rounded down. If you guy by the ultra-high caffeine intake studies (again, in women, and coffee beats tea), you'd expect up to a 3 nmol/L boost.
I think this effect is exceedingly rare. About as rare as a healthy male having 90 nmol/L of SHBG in the first place.