If the website/data is clearly associated with a contract (a license is a contract), it is in that case:
As a consumer, maybe it doesn't matter because there are many exceptions and loopholes for consumers (similarly to how EULA are void for a variety of reasons).
As a company however, company don't get consumer exceptions and are not given the benefits of the doubt, if a company decides to source data/software from somewhere, the company must have done the groundwork to ensure it can use the data and under what conditions. (In case I'm not clear, that means the company automatically read and agreed with the contract when using the data).
>>> due to the fact that it is protected by copyright.
Careful here. I think you might do the mistake of assuming that it's all about copyright and it might be wrong. (One angle is to try to void the contract, claiming that the data/database can't be subject to copyright and the contract has no ground).
Contracts like the GPL and Openstreetmap are not (only) about copyright. They are full fledged contracts with many pages, many clauses, that put obligation on both parties. They really are complicated contracts. They have a variety of grounds inside and outside of copyright.
The Appeal court and CJEU basically dismissed copyright/counterfeit claims in the first precedent few months ago, saying it's a contractual matter (short version, there's some nuances to it).
>>> Reviewing the OSM Legal FAQ, it appears that they are very much based on copyright and licensing.
License is a US legal concept that doesn't exist in Europe. In Europe there are only contracts, US licenses are interpreted as contracts (and if they don't satisfy the local requirements to form a contract they are void).