For your "Wandelen in Brabant" group your issue is due to the upload/publish permissions not being set correctly. You have Photos, Videos, and Wall all set to Group Owner. This means only the group owner can add new content to those. You then have File set to Group Moderator so only group moderators can upload files. It's working as intended. If you want any user that's in the group to add content then you need to adjust those settings as needed by editing the group then adjusting their parameters on their respecting tabs.

For your "Wandelen in Zeeland" group it's set perfectly fine and am able to add new content fine with a registered user. Please note you must join the group first before you can use those features.