Method of data storage isn't really specified, but that's why it's General Data Protection Compliance.
Now if a hidden 30 page long legal document that no one can read is consent then I have this bridge I want to sell. It is totally legit.
While GDPR did raise the threshold of valid consent, the interpretation before the GDPR was nowhere near what you describe here.
There are authority guidelines and sanctions predating the GDPR on this.
I have also talked personally with politicians who was involved with the work of writing GDPR, and the people who wrote the ePrivacy Directive has reportedly said that lawyers interpretation of consent was beyond the imagination of the original intent of the directive, which is why GDPR now require freely given informed consent in contrast to the old consent.