Not rly warden could belive or he could express that urn is only myth but it was forced on him (by plot) and pretty much s/he can said that to sten. As i said no one belived in that nor warden had to (as it is your protagonist s/he can belive in what you want and thanks for that because it is RPG).
Besides that the warden can kill genitivi for that reason so urn could stay myth so warden could in such case just tell that it wasn't truth and pretty much it stays myth...
That seals the deal even more, don't you think so? With no proof that the urn exists, with no other accounting than lore from a thousand years ago, and with a very skeptical Warden that follows the trail just because some nobles are desperate to cure one of their own in the middle of a war, STILL there were people looking for the urn.
So, in a time of peace, following clues left behind by a famous Chantry scholar and with (at least) two nobles swearing that the Hero of Ferelden used the ashes to cure the Arl, is it that difficult to believe that a more pious adventurer (like Leliana herself) wouldn't try to find them with better luck than others before the Warden?
The Epilogue in DA:O provides a good situation for that:
“Rumors that the Urn of Sacred Ashes had been found, and that it was used to heal Arl Eamon of his poisoning, circulated in Ferelden in the months following the darkspawn defeat... slowly, at first, and then with growing frequency as the grand cleric failed to deny them.”
Rumours, rumours everywhere, stronger than ever. Ok, epilogues may not be used when Bioware isn't interested, but since it's Bioware who is interested in using that place for DA:I, that would provide a nice explanation for why anyone looked for and found the ruins. And this is only for an instance where the Warden killed Genitivi and Leliana wasn't in the party (as in 'she wasn' recruited at all').