1) Elly and Character X agree to do something at a certain time.
2) Character X is delayed for reasons beyond human control and cannot reasonably be expected to be able to tell Elly this.
3) Elly runs around in circles formulating escalating doomsday scenarios.
4) X manages to be able to get in touch with Elly.
5) Elly stands there screaming at the poor sap for making her worry and refuses to entertain the possibility that X just plain couldn't get to a phone.
6) Elly spends years holding X's "sin" against him/her.
This, as you will recall, was the whole point of the sequence wherein Liz got caught in an ice storm and couldn't tell Elly what was up. It should also be noted that when other people ask her where she's been when she's running late, she grimaces at them like they're crazy. If there's one thing she can't abide, it's thin-skinned people have nothing better to do than assume the worst.