Secrecy, even well-intentioned secrecy, is the best way to destroy any kind of relationship.

You need to stop giving money or tell them that you're doing it ASAP, otherwise when they find out (and they will) they will not trust you again.

I understand that that is usually the case, but I do not see how being revelead to be a secret benefactor would make them lose trust generally with me.

Because they would have said no if they realised it was you. You're doing something they DON'T want.

Granted, but the only reason they woudln't want me to do it is for my own sake, yes?  It's kinda like receiving really nice gifts from someone and honestly responding with a "You shouldn't have!"  sort of thing.

But do keep pressing your point if you can: damaging our relationship is the last thing I want, of course, and it would be prudent to check everything I do.

I don't even understand what the fuck you are trying to do. I thought English might be your second language from the op but it looks like you are from USA. I don't even know why I am responding to this thread but the main reason is that I just know what the fuck you are trying to ask.  AKA you should never have to produce your bank account number to a  third party.

I can see why this would be unclear, as I'm only giving half the details of this situation out.

What I believe could happen is this: my friends might think I'm the one giving money, and they might ask to see my bank transaction history to determine if their suspicions are correct.  I need a way to hide that history.

It's not ok to ask to see someone's transaction history. Tell them no; it won't be suspicious.

That is quite likely the most realistic thing I could do, admittedly.  I'll probably try that, should it actually come up.

But juuuust in case, you know?

There is no just incase. It is PRIVATE information.  They can't force you to show it.

The only people who have the authority is the law enforcement, assuming they get court approval to see your records. 

Just do what the other crooks in the world do, open an accoutn in teh cayman islands or a swiss bank account as your identity is just a number. But I am pretty sure you need a substantial deposit to do that.

Yeah, they can't force me to show it, but I'm worried that in the conversation that might occur about the topic an refusal to show would be effectively a confession.  Which is absurdly unlikely, of course.  Nevertheless...

Opening an alternative account is a good idea. The only drawback would be that I would still either have to show them my real account (and its Paypal transactions) or I would have to show my dummy account, which might look suspciously recent.  But, it's the strongest idea so far, and I may just use it.