Frankly thank you, thank you very much especially to d.roger and Cyril.f for the interest and help given to this post!
The problem was quite simple as in the most by cases! This is after reading the answers of Cyril.f asking if the paths were identical on all the workstations and d.roger wondering about the presence of the SOLIDWORKS Data folder in the path.
Indeed, on my computer, the trunk view was not installed in the same place as on other computers. I shouldn't have trusted...
Thank you again and see you soon for other twisted but interesting questions!