It's not so much that you "have to" know the source of the funding;
it's that you may"have to" comply with funding requirements imposed
by the source so you better know what the source is.  That's probably
why the accounting office is concerned.

One escape may be a fixed-price arrangement.  That is, if you can be
treated as a vendor then some of the flow-down requirements may not
be applicable.

And if some requirement is not met it may be the case that the
prime source holds your funder responsible (e.g. for not telling you)
rather than you.

But neither of these arrangements is complete protection; your best bet
is to know where the money comes from.  Ask.  It's always a reasonable
question, and your funder should know.

Stuart Ross
California State University, Fullerton