This is correct, but it looks like it is also possible for the receiver (me) to go to the WU US website and (as a guest) set up the transfer with the sender's name and phone number. Then the sender (supposedly) has 12 hours to go to a WU agency and send the funds at the "locked in" rate.
As my sister-in-law has a debit card for my trust account, all she has to to is go to an ATM (often located in the same business that offers Western Union services: 7-11's, U.S. Bank, and Walgreen's (ans many others), get the cash and pay for the transfer, which I will have already set up on line with her name and phone number as well as my name and Argentine ID (CUIT/CUIL). My email will be included in the info I will enter when setting up the transfer, so she shouldn't have to go on line to do anything