The first sentence is very true. And there are many actual scientists who are hard atheists and will use language such as "there is no god". When you have a hypothesis for which no evidence exists and all evidence points to a different conclusion it is really easy to simply use that kind of language. I've used it myself. I've said "there is no god" on many occasions. And I'm probably right.<quoted text>
Science isn't a person. So lets be clear that there are people that use science to try to prove God does not exist.
I believe that use of the scientific method can neither prove, nor disprove His existence.
Your second sentence is true, but with some caveats. On the purest philosophical level you are absolutely correct. Science cannot prove or disprove god...right now. Not with our current tools and level of understanding. But if god exists IN the universe at all then he is within the realm of science and can certainly be shown to exist or be shown to the highest possible philosophical degree to not exist.
The trick is when you place your god outside the universe. If you say he is eternal and transcendent then suddenly he cannot be proven or disprove by science. That is by definition supernatural, outside any possible scope of natural inquiry.
But here's an important caveat. The more specific a god, the easier it is to dismiss. The Christian god in particular is very easy to dismiss because so many specific claims are made that can be looked at scientifically or rationally. For example, the Bible makes a lot of historical claims that are not true. There never seems to have been an exodus, for example.
The god of the Bible is morally inconsistent. It is claimed that he is omnipotent and all loving. Well, given the fact that babies are often tortured and killed, that claim cannot possibly be true.
Jesus is said to have been dead for days then rose again. We have no reliable record of anyone being dead for days then coming back to life. So that's a strike against this god being real.
Stuff like that.