Location services doesn't just refer to the GPS functionality on your device. Specifically in this case Apple requires that we turn on location services in order to access your photos. The reasoning behind this is that your photos could have location data embedded in them already and we have to ask the user if we can access those photos. In a nutshell, we don't use the information for anything, but Apple requires that we disclose the fact that we could.
If you are uncomfortable about this, you may keep Location Services off and create Postagrams using your Facebook or Instagram photos. Your can also leave them off and approve the use of your photos on a case by case basis by clicking "Use album photos".