I think you should ask the developers in the other team how often they get called during their rotation. You should also ask how much of a priority it is within their work scope to eliminate the issues that are causing the processes to fail.
I used to work for a small company that had nightly batch processing jobs on stock data from that trading day. If any one of those processes failed, then someone had to log in and fix it or the company wouldn't have a product for the next day. During the day we had other things to work on, things the business wanted and there was little importance given to fixing the brittle (broken) data processing. Management saw it as working software. They weren't the ones logging in at 3am for two hours to keep the business rolling the next day. That had a big effect on me. I felt like they didn't care about building good software, testing the software, and giving the developers peace of mind that what was in production was well tested and signed off. This is what ultimately led me to leaving that company and joining one which had solid processes: development -> staging -> qa -> production. Because of that process we haven't had a single outage in 3 years. I can go home at night and think about the software I'm currently building, not worrying if I'm going to get an email alert late at night because no one cares about fixing our broken software/processes.
In conclusion, take heed.