Counter-push is not same as defending against push you know ?
And A counter TO push is a different thing. Same goes for turtling.
Best counter pushers are Prophet, Tinker and Lycantrop as they can get very further into enemy territory and push even faster than a whole five man team especially when they are slowed down by four of the counter-pusher's teammates.
Heroes that are counter to pushes are with spells that completely stops the pushes. They need not to be putted in danger meanwhile so they need long ranged, low cooldown nukes that clear creep waves easy from safe distance.
Preventing the creeps to enter the 'BD regen zone' is the best way to stop a push because fighting an uphill battle with a tier 3 tower madly regenerating HP and five angry heroes the same time is not a good idea.
Natural choices are some heroes that can work in pairs - Alleria's Power Shot Puck's Illusory Orb can clear it from safe distance. Vengeful's Wave or Alchemist's Acid Spray with Rexxar's Axes can do the same thing. Some heroes as Jakiro and QoP can stop it with ultimate and similar.
Other heroes depends on items or levels such as Techie (level/Aghanim), Shaker (kelen) and some others.
Meanwhile turtlers prefer to fight under tower with great defensive spells, there are a lot more of them, most of them got stational AoE spells with great duration so the enemy must fight under their effect. Some examples are Dark Seer, Venomancer, Rhasta, Alchemist, Undying, Pit Lord and others.