Pulling updates from the Play Store for the app or pinging its service while being at the wrong place at the wrong time might cause you to disappear.
Even if they aren't doing anything to hide the network traffic, there are events that people want to capture where the main bad actors don't have those capabilities. Taking recent events in Ferguson Missouri, for example, while the NSA could almost certainly tell who was using the EyeWitness app, the corrupt local police almost certainly couldn't.
In that case, compromising electronic communications has been a key strategy in disrupting organization and identifying targets that pose a threat.
We've been very careful about not letting any details leak to the press about our campaigns in the Middle East.
If an app puts that control in jeopardy and I'm in an occupied country, I wouldn't want my Google account listing that I have it installed. Nor would I want to use it on a compromised network.
The little ToS they have you scroll through when you install it makes it apparent that it shouldn't be used on an untrusted network.
Good for them for making it unambiguous.
Most casual/uninformed users won't sideload an application if it's available through an app store.