What accuracy is required in todays ADS-B position reporting?
You can report any accuracy you want over ADS-B, as long as the position source is compliant with TSO-C129 (or later revision), TSO-C145a/C146a (or later revision), or TSO-C196 (or later revision).

ADS-B gives amongst others:


a position, 
an associated Navigation Integrity Category (NIC) based on the GPS Horizontal Protection Limit; and
an associated Navigation Accuracy Category for position (NACp) based on the Estimated Position Uncertainty / Horizontal Figure of Merit. 


If the positioning system cannot provide integrity or accuracy, the ADS-B transmitter will encode the NIC/NAC as 0 (unknown). This warns users of the ADS-B data that the position source is not to be trusted.

In day-to-day operation, ADS-B is required to provide:


an integrity limit less than 0.2 nautical miles;
a reported accuracy of less than 0.05 nautical miles;


Practically, GPS will occasionally give lower accuracies / integrity, but it will be reflected in the NACp / NIC so that users of the data can decide how to handle this lower quality data for their purposes. 

Mobile phone A-GPS chips are typically not certified under the TSO's mentioned above and they don't provide integrity information. These chips are thus not suitable for ADS-B.