I used to work for a small systems integrator. We used on-call mobile phones, the "hot potato" was carried by the on-call engineer. Any actual time worked outside of core-working hours was paid back in the form of time-off-in-lieu. The salary generously reflected the being on-call requirement.

The other factor was that a "call-out" was not completed until the root cause was fixed.

I believe the real reason for the compassionate arrangements was that the owners of the business were former engineers and were even available to escalate calls to them if you got stuck. Our personal phones had everybody else's personal numbers in the address book, but we were never permitted to give them out to clients. Clients only had access to the "hot potato" phone numbers, which also received the various paged alerts, etc.