I think most PhD students publish with their supervisors and only publish without them after their PhD.
If you got an invited paper, presumably that would be off the back of something you already published, either with or without your supervisors. I think that would be ok to take on that paper alone, as long as you didn't need your supervisor's input for anything.
If you sought to publish something outside of your PhD work, then technically that's ok to do that without your supervisors but they might say they are paying your to work on your PhD, not to write random articles.