If what you said were true about teachers making sure everyone got it right there couldn't exist any schools within Buddhism as all would agree. But there are not just many traditions generally but within Zen you find quite a lot of disagreements between groups and teachers. If it is a matter of making sure somebody properly understands the teaching there should be exams, tests and diplomas, but that is only a modern phenomenon in East Asian Buddhism that people study at universities. Also, if understanding can be measured one could even take online tests. Then again a personal instructor would not be necessary.
There is not so much doctrinal variation in Buddhism as you are saying. There are maybe half a dozen broad traditions. Not so much for a 2500 year old religion. For example, when a Hinayana practitioner in India took offense at Xuan Zang's Mahayana learnings, Xuan Zang was able to silence him with his knowledge of abhidharma. Two traditions, geographically isolated, yet sharing enough in common that the two could debate on common ground.
I think Buddhist teachers function more like sports coaches or art teachers than academic professors. That is, you have an ability within yourself that can be brought out through practice. The coach doesn't give you the ability, instead the coach helps you develop it. It's not a matter of imparting knowledge from the learned to the ignorant that can be measured in testing. "A special transmission, outside of the scriptures," remember?
I've heard complaint here that even when one belongs to a center, one has a hard time getting to talk to the teacher. Every group I have belonged to (admittedly all Tibetan Buddhist) the teacher has given regular talks with question and answer afterwards. And the questions did not have to be on the topic of the talk. So if you didn't mind asking in public, you could get whatever bothered you answered.
But I hear from one of the members of our group that in a Zen group he belonged to previously, no one ever said a word to one another. They would meet in silence, recite their prayers, meditate, and leave without saying anything. Sounds like a funny way to run a "community."