But it is this built-in debug "probe" that the JTAG adapter is communicating with. Without debug support inside the chip, the JTAG adapter would not be much use. Support for boundary scan could help factory production, but isn't a real way to debug with.

JTAG is one, of several, electrical interfaces to get access to the internal debug cells in the processor. Atmel have their one-wire debug protocol, playing with the reset line. Or you might have the Serial Wire interface, where only TCLK and TMS of the JTAG interface is used. BDM is another alternative.

But in the end - it's the debug cells incorporated in the processors that allows us to debug without having real emulator solutions or special bound-out chips that exports lots of internal signals besides the ordinary processor pin signals.