I was writing a long response but now it seems the problem corrected itself.
It should have been some cache issue but I don’t think it was the browser’s fault. It may be the proxy I use at work =/.
Anyway. Thanks for your answer but I wouldn’t set the header image manually. In my case, that piece of code is located in custom-header.php and writes the url using get_header_image(), which is nice as it allows people without PHP knowledge to change the header by interacting with the Dashboard.
Again, thanks for your quick answer. Have a nice weekend.