Billpay does not necessarily mean electronic.
I volunteer for a non-profit and am on the receiving end of these "billpay" payments. The system is so fraught with error, it has convinced me to NEVER use billpay.
Let me give a little insight. When you use billpay, there may not be an ACH transaction. It depends on the billpay processor and reciever. AT&T might get it that way, but maybe not! That's a whole different system. If the central processor who handles transactions for many financial institutions can't go electronic, it prints a check and sends it in the mail.
On the other side, AT&T (or my non-profit) get a big old stack of checks with no supporting information at all. I bet you AT&T gets a box of these every few days (EDIT: nope, I read further and found that AT&T should get them all ACH since they are a utility, but the problem is similar anyway due to incomplete information channeled through the billpay system. Read on.) The checks all look the same, but have different formats of "memo" information based on the financial institution. Some are good about passing along memo info, some are not. Usually, it is just a bare check with a name and address and no supporting information.
To make matters worse, the billpay processor will group same "to:" address checks together, despite the "remit to." In my opinion, this is illegal, but they do it anyway to save postage. For my non-profit, it is a mess because we have multiple non-profits at the same address. The billpay envelope comes with whatever random "remit to:" is first in the envelope at that address. So the stack of 10 checks behind may be a mix of multiple institutions if they share an address. It is not uncommon for small non-profits to share an address.
So whomever handles the mail may put the stack of checks in on mail slot and then you hope that the person handling it is prompt and properly distributes the check.
More than once, instead the harried treasurer just cashes the stack not realizing they are different "remit to" addresses. Since banks now just have a reader that only cares about the "amount" field, the checks are cashed to the wrong institution.
This is just one of the many ways things go wrong. AT&T probably doesn't have my little problem, but they have the problem of the "memo" data which shows the account -- if the billpay people put it there at all.