I've explained this to people a couple of times who make the "faith in science" argument. The difference is that you -can- verify it, not that you did verify it.
Your terminology of trust vs. faith is great. I will incorporate it into my arguments in the future.
I think you may have a different understanding of "faith in science" than brobdingnagians. It could mean anything, such as:
1. A belief that the scientific method will definitely approach reality (a realist/pragmatist claim)
2. A belief that the current consensus is right - (but it could be disclaimed)
3. A belief that science will explain everything, so one could discard other studies, such as philosophy or theology.
Each of these positions can be disputed and may be wrong (especially since they were not acquired by the scientific method, but arrived at by philosophical thought), so to some extent you need some "faith" to accept these statements to be true.
No scientist believes position 2 in general. Regarding particular subject matters and well-confirmed theories, on the other hand, it's pretty much uncontroversial. No cell phone would work and no plane would fly if the underlying physical theories were flat-out false.
Position 3 is probably analytically true, too. The idea that there is something that can in principle not be explained by taking a close scientific (=skeptic, methodical, experimental, precise) look at it hardly makes any sense.
I would agree on position 1, but there are many different possibilities it were not true, such as if you were living in a simulation.
My point 2 was not supposed to mean that current theory was wrong as much as there (most likely will) be a more accurate better theory that will replace current ones. No-one disputes that (non-Microsoft) cell phones work. The problem lies on the philosophical side - Newtonian mechanics caused a big problem in that it was quite strongly suggestive of determinism. But more underlying theories, such as QM make the situation more difficult and complex. Assuming the current or fashionable theory of the time is correct is very likely to lead to a temporary or fashionable philosophy.
Position 3 - Science is an empirical study of reality - it cannot in any way explain why it is not some other reality, for example. If it is governed by logic/maths, unless every mathematical construct has physical existence (which is a rather weird and unrealistic idea), you cannot explain why this mathematical construct has existence and another does not. You may argue that other studies may be pointless, but you definitely cannot claim analytically and for certain that science can ever explain everything - so this is the point at which you are bringing in an unreasonable faith in this case. And science without study of philosophical implications is rather shallow and cannot give a reasonable mind satisfaction (not that philosophy is satisfying).
Your terminology of trust vs. faith is great. I will incorporate it into my arguments in the future.