I think you're being pedantic over the meaning of words; true, a website that announces being up 1 minute per year and is up 1 minute per year is 100% reliable. But in common discussions, reliable really means "up and running".
Now, maybe you're right and we should be using another word, and aim towards less uptime ?
Well, maybe that's pedantic, but reliability has a precise meaning that means hard money through service level agreements.
So yes, it's worth it to be specific over the difference between being available and being reliable (== meeting expectations, including being unavailable at times).
If I claim a 99.5% uptime SLA guarantee for my webservice and that it does, it's reliable. However, 0.5% of the time, it may be unavailable _and that's not an issue_.
Now, maybe you're right and we should be using another word, and aim towards less uptime ?