I think this is just a matter of semantics. Are you saying we should call a black-car hailing service "ride sharing" simply because you booked it with a smart phone app rather than calling a number? (Remember that Uber didn't even use a novel business relationship; there have long been dispatchers with a single phone number that distribute the rides to multiple independent black car agencies.)
To me, the key change deserving a new term was allowing completely independent, non-professional drivers, and I think Lyft beat Uber to that. (Heck, some purists would say "ride sharing" should be reserved for cases where the driver doesn't make an wages, just reimbursement for costs.)