Khan Academy is soliciting donations, an avenue of human interaction which asks us to suspend this local rationality and instead transact on hope and trust. That's the difference to me between a business transaction and a donation.
Hence, you're not being asked to "transact on hope and trust".
The main difference between donating to KA and a typical business transaction, is that the value of the goods/services provided does not necessarily go to the person providing the payment.
There is an understandable worry about over-payment of executives, but I don't think that the "threat model" is significantly different between for-profits and non-profits. You could argue that in the case of for-profits, competition will weed out companies that over-pay their executives, but internal, corporate politics is likely to trump the market mechanism — at least that's what seems to be happening. As a result, I don't think that it makes sense to excessively harp on executive pay at non-profits you donate to, or at least not more so than you care about the pay of the CEO at a company whose products you buy.
> [...] transact on hope and trust.
These two things are not as dissimilar as you seem to think.
There is nothing irrational about donating to a non-profit, and nothing irrational about paying high salaries to irreplaceable employees or executives.