There is an app called bodyweight fitness on the play store without any permissions. It is available on git hub as well: https://github.com/mazurio/bodywei
This is because the INTERNET permission is a "harmless" permission. This means that you don't have to ask the user for permission, and that it will not show in the Google Play Store
Since Android 5.0, permissions have a "protection level". Some are dangerous, and some are normal. Normal means that you as an app developer do not have to ask the user for permission, and that it will not show in Google Play. Dangerous means that Google Play displays it and that you have to ask the User for permission.
Source and further reading: Android Developers