Hello Ichthus,
I think you are mixing up NOT investigating with not being able to investigate.
Technically, you are asking them to take them on faith. A student may not always see his teacher's diploma. The student therefore has to have faith that either
# the school did a good, thorough search on their teachers
or
# the teacher actually did pass his/her collage classes.
That simply isn't how it works. You are correct that most students never see their teacher's diploma. Most take it on faith that he/she has one. They have evidence to support this, after all, the school would have to see the teacher's qualifications, before hiring. This is much the same as assuming on faith that when you fill up your gas tank, you will get fuel from the pump and not raspberry jam. You could empirically examine the pump before filling up, but it wouldn't be practical or sensible.
The essential difference between your example and science is that the students in your example CAN look at the diploma. It is real. They can look at it if they want to. They don't bother to look because they don't have the time to investigate every situation in an empirical way, the same as you and your gas tank.
Science on the other hand, does go to these lengths. A scientific investigation of whether your teacher had a diploma or not, would most certainly involve someone looking at that diploma. Assuming good faith would not be sufficient. It might be expedient to simply trust the school to have hired the right person, but that would only be done where the hiring process had been independently checked and verified (a process comparable to the peer review process).
Scientists take nothing on faith. Wherever there is a claim in science, it can be traced back to the original data.
With religion, thee is no way to trace back to the original data. There is no evidence behind the claim. There is only the appeal to faith. If you decided to investigate your teacher's diploma, you could. If you decided to empirically investigate God (or any other article of faith) you will find nothing beyond faith.
This discussion touches on the issues raised here by Subbie
Message 1. I particularly recommend Modulous' summation of the reasons why science does not appeal to authority in
this post.
Mutate and Survive