Apparantly you are using a microflow to access the data. In this microflow you can Always add a split which gives you the message you want. Or are you expecting deeplink to do that for you?
Is BB only seeing the page? Or also the data?
Andrej you seem to have drawn all the right conclusions yourself. You cannot adhere to the DRY principle here.
Also, realise that the content of pages cannot be considered secret. So if it is really a huge issue that a user is able to access a certain page, then your entity access is probably considered wrong (or you should not be using Mendix in this case).