Thanks for you feedback.
For everybody reading this in the future: multiple checkboxes in Hubspot forms who are getting preloaded and changed by the user, do alter the data while saving. So if you need the form data 1:1 stored with your contact you have to use workarounds. currently there are two:
1. use additional fields and have workflows ready who do the job and. copy the data into the right spots
2. use your own (html) form and save the form using the forms api.