What did they mean...? Interpretations!

[The Saucepan Man]

What I think is interesting, though, is Tolkien would consider such things as a source of 'power'. Exactly the opposite of what Sauron & Saruman consider 'Power'.

Precisely, davem. The likes of Sauron and Saruman think of Power in terms of physical strength, force of arms, possession of magical items etc. And so they do not recognise the quiet, determined and resilient strength sitting there in an obscure region of Eriador, whereas Gandalf of course does. They both make the same mistake of first overlooking, and then underestimating, Hobbits and this accounts for much of their undoing.

While I would not wish generally to lump Boromir in with Sauron and Saruman, the same might be said of him on this point. He sees Power in the same terms and so thinks of it as folly to send the Ring into the Enemy's backyard in the hands of a Halfling. His brother, on the other hand, recognises the power in Frodo and Sam and their suitablity for the task in hand, and so lets them go.