This isn’t a case of No True Scotsman. There really is a right way and a whole lot of wrong ways to do Agile development. Any team that calls itself an Agile team that doesn’t actually follow the processes properly is doing it wrong and will fail.
That doesn’t mean any team that’s doing it right will succeed, but it’s like riding a horse: If you only climb halfway up the horse and try to hold on while at a 90-degree angle, it’s not going to work, and it would be stupid to declare that the concept of horse-riding is broken. No, it’s not broken, you’re just an idiot who thought you could ride a horse while only halfway up, clinging desperately to its side.