Green power is a feature of Zigbee pro. The feature can be used in conjunction with several profiles. All zigbee profiles require a coordinator to establish the network except Zigbee Light Link.
You need a router because it will create a proxy for the green power device. This is how messages can be processed for it even though it is offline until activated.
How does ZigBee PRO Green Power feature work with ZigBee PRO networks?
By creating proxies in a ZigBee router device, each ZigBee PRO Green Power device is represented as always present on the ZigBee network – even when it is not powered on or present. These proxies forward and resend packets to ensure reliable communication, especially to destination devices, called sinks, that are not in the direct radio range of the Green Power device.
The green power device will not be online to process the ACK that comes back, so the proxy has to do it, and resend the message if necessary.
Detailed explanation here:
(btw, you were replying to a post which is two years old now: June '14 means June 2014. But the required router is still the same. )