being a PM doesn't require a title, to be successful in whatever you do these days you should treat each given task as a project that has clear objectives, deliverables and timelines while considering available resources.
so to answer your question in a diffident way.. who deserves the title of PM in my company.. Many.. but who actually holds the title of PM and deserves it.. few.. in percentage wise..20% if not less.. which also includes myself as to an extent I believe I am a capable PM that earned my title through demonstrating considerable Project management skills.