Well it becomes ambivalent when, as the poster above me pointed out, that the information on the LH website wasn't updated and wasn't very clear (German and English had different information on the website), hence my question.

So, in any case, that's an update then from when I last looked, and a step in a good direction. Before you could only skip proof of negative test if you were doing non-Schengen to non-Schengen flights (transit FRA) and your destination didn't require any tests.
How about if, as in your flight example you gave, BOM - FRA, would transit in FRA and onwards to MEX. If I recall, flying in from India is not considered a "clean security" and it wasn't as clear cut to transfer. Would you in that case be considered to be entering Germany or is there a possibility to do a transit without clearing the international area in FRA?