OK, so certain documents are allowed to exist out there; they are not banned. But if you train a mathematical function to provide a very clever form of access to those documents, that is banned.
That is similar to, say, some substance being banned above a certain concentration.
Information from AI is like moonshine. Too concentrated; too dangerous. There could be methyl alcohol in there that will make you go blind. Must control.
Training that function is not banned. Concentrating information is not banned. I have no idea where you're taking that from.
Only making use (i.e. putting into service a product containing it or placing that product on the market) of that function in a manner that is listed in article 5 (which is quite terse and reasonable) is prohibited unless covered by an exception.
Making use of that function in a manner that may be high-risk (see article 6 and annex III, also quite terse and reasonable) leads to the requirement of either documenting why it isn't high-risk or employing measures to ensure that the risk is acceptable (see article 9, item 5).
That is similar to, say, some substance being banned above a certain concentration.
Information from AI is like moonshine. Too concentrated; too dangerous. There could be methyl alcohol in there that will make you go blind. Must control.