|I'm sure you all recognize the quote...|
The agent, Janet Kobobel Grant, explained that having publishers send the entire amount to the agent, instead of her 15% commission to her and the author's share to the author, was really for the author's benefit. She could check the amount (she didn't explain why a statement wouldn't do just as well) thus saving the author "happily skipping off to the bank to deposit an incorrect check".
This picture of the naive little author saying, "Ooh! Money!" and in her enthusiasm failing to notice it was the wrong amount is typical of the patronizing way writers are treated by the publishing industry. We are told there are all sorts of things we can't possibly do for ourselves, so we need to pay most of our earnings to others in order to get them done for us. Of course this learned helplessness is handy for getting rights-grab contracts signed - don't worry your pretty little head with the details, just sign on the dotted line.
When dealing with professionals, it's best to bear in mind that you care an awful lot more about your job than they do. Whether it's a plumber, a solicitor or a literary agent, to them you are just one customer among many.
I've learned not to let other people do my thinking for me. I still remember the time I paid a for an opinion from a QC on the advice of my solicitor. The combined hourly charge was mind-boggling. I mentioned a possible problem I'd noticed, and they shook their heads in unison while reassuring me. I turned out to be right, they were wrong; they moved on to the next client and I paid for their bad advice each month for the next nine years.
Look at the comments on Janet Kobobel Grant's page from grateful authors agreeing with her. Then check out the comments beneath Passive Guy's post. It's herbivores and carnivores.
Don't be a herbivore. They'll chew you up and spit you out.