The reason I use the word true is my amp has been dyno'd and it produces 1200w at 1ohm and I am wired down to 1ohm. My speakers are 300w rms each I have the amp equally feeding each sub their rms wattage.
Those amps that have those claims don't go anywhere near that the reason I know there's several creators on YouTube who have amp dynos Steve Meade, Big D Wiz etc. Big D Wiz buys and dynos amps as a hobby on YouTube he bought a $69 1200w amp off Amazon by Boss Audio it produced 210w that was it but quality amps like Sundown, Orion they meet or exceed their numbers he dynod 2 3000w amps one from Sundown one from Orion the Sundown was spot on 3007 watts IIRC the Orion HCCA 7000watts it has two power cables its a power hungry amp but not power efficient.