First, I want to reject the premise of this thread: not every other race can't provide refunds. Some can, and some can't. Some can, but don't. Every race is unique both in its circumstances and goals.
That being said, many of the reasons Boston can refund (and is choosing to) have been illuminated above. To sum up:
1) Per the 1099 above, the BAA has a cash reserve that looks like it's nearly exactly equal to one year of its operating budget. This is a best-practice for non-profits, but not all of them abide by it (or are even able to generate those funds). What that means is that the BAA could go through one year with no revenues and still pay 100% of their expenses before running out of funds. Would they want to do that? No. But could they (disregarding exact cash-flow and expense-cycle quirks)? Yes. That they have the cash is the biggest reason they can refund (because if you don't have the cash, you can't!).
2) Because Boston has a true, hard cap on number of registrants, and actually turns away qualified runners every year, and for many folks running Boston is a once- or very-few-times-in-a-lifetime event, the BAA knows that both very few people will take them up on their offer, and also that they will be able to back-fill those limited slots with paying qualified runners who were originally rejected. And even if the refund "take rate" is higher than anticipated and the BAA doesn't quite fully fill the field--which is unlikely, and also they also have other ways of filling it besides qualifiers--they can cover a small hit out of their cash-reserves. (This would likely lead to them making some decisions in that would allow them to re-build that cash reserve in future years.)
3) I think someone else hit the nail on the head by noting that if you don't take your refund when it is offered now and the race is canceled or otherwise substantially altered (elite-only, or elite and virtual) in September, the BAA probably feels it has a pretty good leg to stand on in not offering you a refund then. In their mind, you knew the risk of cancellation existed (how could you not after so many other events have been cancelled?) and turned down their offer of refund thus knowingly assuming the risk yourself. This may not be fully decided internally, but I bet it has played into some folks' thinking.
Other races may fall in a different place in any of these categories, and so they may or may not be able to (or may or may not choose to) refund based on that (or on where they fall in numerous other unnamed categories).