Isn't your thinking that you can't take anything to manipulate shbg also a belief?
Consider this.
1) We don't often measure SHBG, so we don't know how often it changes.
2) Free testosterone reflects shbg, but that test is known to be unreliable. So changes in free T could reflect changes in shbg or just test variations.
3) Shbg seems to change very slowly, taking months to change.
4) It's proven that various drugs can raise SHBG, a few will lower SHBG.
5) Insulin has an inhibitory effect on the SHBG production in the liver.
My shbg seems to be pretty stable for 5 years at 35-42, but when I started taking LEF ultra prostate supplement, after 4 months my SHBG had rose to 66.2, I stopped taking the prostate supplement, a month later my SHBG continued to rise to 73.6 (which really surprised me). But 4 months later SHBG dropped to 57.2. So it seems some herb in the supplement caused my SHBG to rise, but both the rise and fall were pretty slow.
I am sure a confounding fact will be what are your levels of other hormones/minerals? I supplement with boron, magnesium, B vitamins and my Vit D level was tested at 90.6. I am sure a person that is low on these items will react differently to the same batch of herbs that a person with high levels.
With all these moving parts, it becomes nearly impossible to determine how an individual will react to various supplement/drugs.
I haven't used any supplements to lower my SHBG, so I have no experience with that.