"Weel done, Cutty-sark!" -Mithril, Moria and Valinorean ship-building

[Morwen]

"As a matter of fact it was all mine. Except that Aragorn insisted on my putting in a green stone. He seemed to think it important. I don't know why. Otherwise he obviously thought the whole thing rather above my head, and he said that if I had cheek to make verses about Earendil in the house of Elrond, it was my affair. I suppose he was right."

FotR, Many Meetings

This statement suggested to me that Aragorn was content to let Bilbo be. It is after all a poem, not a historical treatise. If Bilbo wishes to describe Earendil's ship as being made of mithril, Aragorn might wonder briefly where Bilbo got that notion but wouldn't spend a lot of time arguing with him about it. I mean are mithril ships any more far fetched than say, elven warrior princesses?