Well, game piracy has been around for decades, and the industry is still alive.
If anything, piracy greatly helped Sony to move PS2 and PSP consoles in such numbers.
When they say it's "threatening to kill the industry" they really mean "threatening to cut into our bottom line." As you've said, the PS1 had RAMPANT piracy, and it did little to nothing to hurt it's sales in both hardware and software.
The truth about piracy on consoles? Less than 5% of owners do it or even know how. This is a case of greed and profit margins, not the death of the industry.