A Dutch speaker read Afrikaans without too much effort; understanding spoken Afrikaans is a bit harder, but depending on the person it can be fine.
A Dutch speaker can't read or understand German. Some words are similar, but the same can be said about English. There are a number of differences in the grammar and alphabet.
Of course they're related languages; because I can speak English, German, and Dutch I can kind of read Swedish or Danish on account of being Germanic as well. But that doesn't make a "dialect with pretensions". We might as well say that all current Germanic languages are some sort of "dialect with pretensions" of some old Germanic language. But that doesn't really mean anything.
> A Dutch speaker can't read or understand German.
A Dutch speaker can't necessarily read or understand German. However, a Dutch person nearly always does, and often flawlessly so.
This is just wrong. I have nothing more to add, because this is just not the case. Maybe it was true 60 years ago, but not today.