"the pyro equivalent of a chainstab"

Yes, compare pyro to spy, you'll see pyro is obviously overpowered...

Spy has invisibility, a little more speed, backstabs and a revolver.

Pyro has more hp, fire resistance, airblasts, (random crits, snowball crits or backburner crits), don't have to aim, can fly or have a shotgun/flare/etc and he can remove sappers.

If the pyro goes behind your lines, the round is over : you have to chase him or you will be backburned in few seconds. And to chase him, a scout a pyro or a soldier is not enough. You can try with a sniper, but a good one because pyro's head can be hard to reach.

If the pyro is keeping enemies sentries, you have to wait an ubercharge (and pyro can airblast ubers to defend sentries).

One more thing : 2 spies in the same team will "embarrass" themself. 2 pyros in the same team can "outsmart an entire team".