It's not cheating if they intend for you to do it (but just can't explicitly
say it's allowed because then
everyone would do it and that would collapse their self-assortative price-discrimination strategy.)
> If you can "cheat" on getting the discount, people just keep finding reasons why they are justified to cheat. "They should toughen the verification procedure if cheating is possible".
You seem to misunderstand the argument. It's not "they should toughen the verification procedure if cheating is possible." The argument is that they would toughen the verification procedure if cheating were possible and they cared; which proves, at the very least, that they don't care (and potentially proves that they in fact want you to do it, at least sometimes.)
To be clear, this argument doesn't apply to bureaucracies — governmental, academic, or Enterprise — where there's so much red tape in the way of making changes that it's almost impossible to fix issues like this even if several people care quite a lot.
But this argument very much does apply to a relatively-agile, not-so-Enterprise-y-for-its-size corporation like Apple. In fact, it applies especially to Apple, who has an almost Disney-like obsession with micromanaging all customer interactions as an extended customer-lifecycle marketing opportunity. (For example: you'll never find a rotting out-of-date page on an Apple-owned website.)
Apple know exactly who they're giving this discount out to. They've almost assuredly sat down at least once and done a hand-analysis of one or more months' purchases, to determine the proportion of education-store purchases that are from genuine education customers. (Heck, they probably have gone far beyond this; far lazier corporations than Apple set up heuristics for this kind of "promotion fraud"; run continuous analyses on them; and spit out a weekly reports to mull over in marketing-KPIs progress meetings!)
If Apple's education store gives discounts to group XYZ, then you can assume that that's the intended outcome. At least under the Apple marketing department's current paradigm of thought.