On iOS, Apple made it so the app has to get permission to access the phone book. (Interestingly, Google Image search turned up this for a query of "ios address book permission": http://i.stack.imgur.com/MHF0p.jpg)
Did OP give this permission? I'm not defending Path (at all!), just trying to get full details. I've in fact accidentally given address book permission to apps by tapping too fast.
Apple added this feature after the previous privacy gaffe from Path. Still though, there's a legitimate use case for asking for your contacts, and it is to help connect you with people you may know who are also on path. You also give them access to your photos to share things on Path, but there would be an uproar if they started uploading all of your photos to their servers. I'm not really seeing any good way to solve this at the OS level, it seems the only solution is for apps to be less shady.
However, according to Apple, even before iOS6 came along (which asks permission whenever an app requests access to Contacts) it had already been against Apple’s dev guidelines to use Contacts info without users’ permission:
“You and Your Applications may not collect user or device data without prior user consent, and then only to provide a service or function that is directly relevant to the use of the Application, or to serve advertising. You may not use analytics software in Your Application to collect and send device data to a third party.”
Interestingly, Android was much better about application permissions for some time. These days though, it seems iOS allows users to have more control.
On iOS, for reference, one could install Path but then deny it notification permission (or limit what types of notifications at a very granular level), allow/deny access to photos, and allow/deny access to the address book. You could deny all of those and still use the app just fine, though obviously without the ability to upload things from your photo roll.
Did OP give this permission? I'm not defending Path (at all!), just trying to get full details. I've in fact accidentally given address book permission to apps by tapping too fast.
Update: OP is using Android, which is different.