Or is 'the computer told me so it's correct' good enough these days?
The same way you determine if a professor is knowledgeable -- they are employed by a school with certain level of reputation that you are comfortable to attend.
A good university will be full of smart people, student and teachers alike. You essentially learn by contact. There are also rich and influential people, who can provide you with great job opportunities.
It all goes hand in hand: the brand, teachers quality, student quality, the infrastructures,...
Worse teacher may affect the brand negatively, the smartest students may want to go elsewhere, the rich, who want to be with the smart will leave too, which will affect funding, meaning less infrastructure and be less attractive to the best teachers and researchers. It is all connected.