No one who is in engineering would say something like this. I can only conclude your job is auxiliary to engineering. In which case: I don't think someone who isn't an engineer should be talking about what is and isn't possible with respect to how engineers work. It's also a good idea that when engineers do tell you how they work -- not to ignore everything they say. Since Afterall -- you're not actually the one doing the job.
I am a software engineer and most of them I have met throughout my career do not work on tasks that require 24/7 silence. Basic communication is important for every task and if you cant handle that you are simply not suited for the job.
Urgent message! Do you have a moment for a quick call? [It's never quick.]
Urgent message! Hi $yourname.
Urgent message! Hi, so I hit this problem where this-and-this doesn't work. Here's an irrelevant part of the logs. We need to sort this before deployment tomorrow. [After couple of these, eventually your PM tells your team to stop fulfilling such requests from other teams, and instead first ask what the billing code for that is, or if they wouldn't rather file a Trac ticket.]
