Can you send a screenshot of the capabilities around assets. Good to know that the capabilities in the group are additive, make sure there is only one for assets.
You can also ask the user to inspect which group he is member to as well as the capabilities through the Access info at the bottom left (User name)
@Gaetan Helness! Good to know that. Your explanation was very helpful. I was wondering if it's possible to restrict data deletion, allowing users to add and update assets but not delete any data.