I think a better analogy to use would be a very slow loading app.
Say your app takes 5 minutes to load the first page and 1 minute to switch between pages after that. Instead of blaming the developers, blame the users for expecting too much of the app. Personal responsibility and all that.
It's the users fault they are using the app during peak times. If they really needed access to X part of the app they should have done it before it got busy.