I just looked into the app being used here, called “covenant eyes” and it seems your interpretation of the phrase is actually more correct, unfortunately that makes the headline even less misleading. You are indeed able to see and review exactly what content was accessed that set off the alert.

If you watch the “How it works” intro video on their site it seems they are literally monitoring and reviewing each other’s porn intake.

No, what monitoring in this context means is to be made aware of each other’s porn INTAKE, or how much is being consumed and when, which the software is said to do. Nothing is suggesting they seek porn out to share content with each other, just that they are alerted when the other accesses porn.

I’d bet youre right about the alternative devices though.