Core Routers Are Used For Transition Purpose

I was watching a video that mentioned that core routers are used for transition purpose. In a service provider the purpose is to route traffic unlike an application provider in which it is a destination.
In that case why can someone ping the core routers even though they only label switch packets?
In that case why can someone ping the core routers even though they only label switch packets?
Comments
In regards to your comment about label switched packets, in an MPLS network usually the core routers would be P routers (thinking of service providers here). On a P router the only routes in the global routing table will usually be the loopback addresses of other P or PE routers. P routers only switch labelled packets so they only need to know about the LSP between the ingress and egress LSR and because of this there is no need for a P router to ever know a customer routes because they only need to know how to forward on the LSP between the PE routers that the customers are connected to.
This is a bit of a simplified explanation, If you want a good understanding of MPLS and how it works I would recommend reading MPLS fundamentals. Im nearly finished reading through it (the first book I have read on MPLS) and it is VERY good at explaining the concepts and has a bucket load of config/scenarios that you can lab out.
FYI: You of course will be able to ping the P routers IP from a PE edge router in the same network. Generally though the loopback addresses of P routers are not exported into the VRF on the CE device so these routes will generally not be seen from a customer point of view.