Earlier quoted context omitted.
The app didn't write the error message, the people implementing the app did. Any error message is just as much a form of communication between them and me as it is between the app and me.
But we can't identify which human wrote the message. There's a huge difference between a push notification that says: > Flight UA569 has been canceled. We apologize for the inconvenience and we will rebook you on the next available flight. and one that says: > Flight UA569 has been canceled. I apologize for the inconvenience and I will rebook you on the next available flight. — Alice
Yes, there is a difference in the two examples you gave, although it would have been nice if you had been more specific about what you meant. What I notice is that the first option the apology comes from the company and the people in it, and intended to imply they see it as their responsibility to fix things. The second would imply that Alice is personally to blame for the cancellation and taking responsibility. Either are technically possible, although the latter seems very unlikely to ever happen.
What I fail to see is what this has to do with the error messages. The example given was "Sorry, you do not have permission to access this feature. Please contact your administrator for assistance", which falls under the first form. This seems appropriate for a message representing a team of people who wrote the program, as well as the administrator. It also is quite representative of the apology style seen in such messages.