Usually this is less being outright deceptive (saying you're up when you know you're down), and more wrapping the definition of "down" in legalese so that nothing short of a complete system outage of every aspect of your service for 100% of users counts as "down".
In those cases status pages are more likely to have a lovely spectrum of yellows and oranges to choose from, but a distinct absence of red, but very few companies will say that they're fully green when they know there's issues. Green when you're down is usually more of a symptom of process problems in how outages get reported or resolved (no documentation, manual processes for updating, long communication chains from support teams to engineers).
