Strictly speaking ADS-B does not require GPS / GNSS. But practically speaking, a WAAS GPS system is the "easiest" way to comply with ADS-B's performance requirements.
Many ADS-B systems are sold / installed with integrated GPS receivers. So it is not necessary to retrofit the aircraft's legacy NAV system just to have ADS-B Out.
The two systems could remain independent of each other: one system for navigation, one system for position reporting. (And there could be significant deltas between them).
That's supported by the fact that the coordinates sent as it turned onto the runway at Viru Viru were offset by approximately 1 nm SSE, so it's likely that at least that much error will apply to the subsequent ADS-B track.
1nm error is well outside the limits specified for ADS-B. The position limit is 0.05nm with an integrity bubble of 0.2nm. These requirements can be tough to meet using legacy inertial or RNAV sources, which is why most ADS-B retrofits will include GPS instead.