It's unlikely that Venat went on the run based on her decision to reach out to both the Convocation and Azem in order to express concerns regarding Zodiark which was shown briefly during the delve into the remnants of Anamnesis Anyder.

As of Endwalker, we also know that Venat was simply feigning concern over Zodiark and that it was actually an effective plan that would keep the Final Days at bay for a very long time. Quite simply, Venat didn't try to be truthful or even inform her people of what was happening behind the scenes - nor was it ever reasonable for the Ancients to ever believe of their own accord that an unhinged bird-girl had flown into space to slowly kill any planet with life left on it.

The main reason it doesn't make sense is because the writers decided to tie Venat directly and indirectly to pretty much every bad thing that has ever happened in the story...which robs not only Venat of any real agency but pretty much every other character as well.