This is very possible.Frighteningly possible!I have also thought about it but its very dreadful.If your theory is right,then....may God help us!!!
This theory may be related to anxiety,stress and panic attacks.Maybe after all tetracyclines have nothing to do with it(although being a suspect).Its possible that excessive anxiety causes the body to lose the sense of when to go defecate.Maybe this theory is related to nervous system abnormalities that interfere with the normal functions of the sphincter muscles.Who knows...?
Only assumptions is that we can make.
You say "Maybe the solution is to strenghten and train the pelvic floor and sphincter muscles."
If it where in my power to do it ,I would have done it in first place.To be honest,your theory was one of my first thoughts about the cause of the problem.But,how on earth can this be done?