It sounds like an autonomous behavior that I think is a bit excessive indeed. My pets in real life don't come to me begging to play fetch with them. Hrmm.. I might look into this and see if it is possible to do one for PETS.
*Edited*
Going to test a new mod to see if playing fetch is stopped autonomously. Check back for details later.
*Edited*
New shiny now uploaded for download:
No Autonomous Play Fetch - PETSEnjoy!