I haven’t heard that before but I don’t work on hair care products very often. Benzyl alcohol is used as a preservative in lots of cosmetic products though. It can be considered an allergen for some people, but overall it’s pretty safe (as far as we know so far).
It looks like the 91% natural ingredients version has benzyl alcohol as a preservative which is typically synthetically derived and in my experience can drastically shift the bio-based ratio.
As far as I can see, the rest of the ingredients are the same, but the sourcing of those ingredients could be different which could also shift the naturally derived percentage.
I think what you said is true but that also ketchup as a material is shear thinning—meaning as you shake or tap the bottle, this creates stress or “shear” on the liquid which causes the viscosity to decrease. It also takes a little bit of time for the liquid to re-thicken, so it will actually pour pretty well a few seconds after shaking it.
https://www.scientificamerican.com/article/ketchup-is-not-just-a-condiment-it-is-also-a-non-newtonian-fluid/