In general, this is not correct.
There is no direct equivalent high school in the German school system. The closest to high-school graduation is an abitur.
This is called Hochschulreife¹ (suitability for academic education) for a reason.
Common interpretation of §12 of the German constitution is:
If you have an abitur, you may only be excluded from studying due to place restrictions, in which case the restriction is primarily based on your abitur grade (numerus clausus), but can be bypassed by waiting and other qualifications.
The latter primarily applies to some subjects like medicine.
There is a plethora of bachelor’s programmes that have no restriction at all (besides requiring an abitur).
Admission to a master’s programme also is not grade-based in general. You will probably always have a restriction on the content of your bachelor’s degree though.
With a quick search, I found a programme that automatically admits all graduates from the respective bachelor’s programme at the same university and has no grade-based restrictions for others.
That being said, you will probably find more grade restrictions for master’s than for bachelor’s programmes for the following reason:
On the one hand, bachelor’s programmes are subject-specific in Germany and occur in a similar setting than master’s programmes².
Thus your degree in a bachelor’s programme is a good predictor of your success in a master’s programme of the same subject.
Moreover, most grade thresholds are comparably lenient in light of the common grade inflation.
If your bachelor’s grade does not suffice for admission to a master’s programme, this usually means that you barely made it through your bachelor’s.
In that case it is reasonable to assume that a respective master’s programme is not the right place for you.
On the other hand, since the abitur is not subject-specific, it is not a good predictor of your capability of studying certain fields.
For example, I have seen students with an excellent abitur (particularly the math section) giving up studying math, because they were bad at proofs and this hardly played a role for them before university.
By contrast, somebody with a bad abitur may excel at studying math.
You may also want to read the Wikipedia article on academic admission procedures in Germany.
¹ Hochschule: university or other institution of academic education. There are no equivalents to colleges in the US/UK. Reife: maturity, suitability. Combining these two, Hochschulreife translates to suitability for academic education.
² The separation of bachelor’s and master’s is only around twenty years old in Germany. Most current bachelor’s and master’s programmes originate from a single big programme (Diplom) being split.