As a blockchain developer of 2 years who understands the principles behind Tendermint and who has build many scalable systems in his career, I can say for sure that Tendermint doesn't add any scalability to any given blockchain. It only aids with certain specific interoperability scenarios (nothing to do with scalability). The statement on their website is not accurate. The people who wrote this statement are marketing people who do not understand the first thing about scalability of any system. The leaders of these projects wash their hands of any responsibility by pretending to believe their own dogma.
Most blockchain marketing is a flat out scam IMO. As a result of all this deception, almost everything that everyone knows about blockchain today is wrong. Everyone thinks that all the trendy cryptocurrencies can scale but they can't. None of the ones that I analyzed in the last 2 years could scale. And I looked at many; for those whose whitepaper made the most sense, I even made the time to discuss the tech with their lead developers, node operators and community members. The reality is always far behind the marketing.
Unfortunately, investors are investing based on hype and their personal connections, not based on demonstrable facts. Investors are being mislead en-mass. As a developer who understands the tech and who actually believes in its potential to incentivize productive collaboration, it's disturbing to watch how the industry is unfolding.