Where have you seen this? I'm pretty sure that people's belief, while powerful, also relies on knowing what the thing is. The question would be: Can an object of belief be powerful without people knowing they are believing in it? That's not quite the right question either. Basically, if I believe that a nail from the cross is Holy, but as far as I know you are just holding a sword, does it matter that I and other people hold that belief. There is not actual object to focus that belief on. When we see Harry use faith to light his amulet he is focusing intently on the amulet.
The other side of this is that I think we have a pretty good set of indicators that there really is a God out there in the Dresdenverse. Though not by any means a Christian himself, Harry certainly believes He exists. There may actually be power bound up in these swords... it's a tough call, but I'm curious to learn more in the future.
Unfortunately, I don't have all my Dresden books handy to quote passages to prove my case, (They're on the another coast) but I can try my best to at least put my point of view into perspective. I will admit I could be wrong about this, but I stand by it until a better explanation comes along. Right now my opinion of Faith magic boils down to Consensus Reality.
Harry explained about Faith magic in like Book 3 or 5. He explained that the magic of wizards works because the Wizard believes in his/her own magic. He then explained that the magic of Faith works because a lot of people have Faith in God. I do not question or dispute the existence of a God in the Dresdenverse, but I personally think that Faith magic works not because it comes from God, but because enough people have Faith in that God.
I think this because I interpret Faith Magic as being linked to the philosophical idea of Consensus Reality.
Consensus Reality in a nutshell(Not a completely accurate description) is that somwthing is true because enough people say it is true.
For example: Currency is valuable because people say it is valuable. A $20.00 bill is worth $20.00 because society believes it to be true. If I came from a primitive society without a concept of money or currency I would see a $20.00 bill for what it is, a piece of Green Paper. However, regardless of what I believe a $20 bill is worth that much because society says it does. The Consensus of society sees the piece of green paper as valuable and therefore it is.
I probably butchered that explanation, but anyway.
A lot of things in TDF work on this same philosophical principle. Thresholds work on this principle, Graveyards holding in spirits because of this principle, and in my opinion objects of Faith. There is Faith magic in the air because people have Faith and the nails in the sword are a part of that Faith. Those nails are acting as antennas for all of that Faith Magic in the air because they are linked to it. When you read about the Cruxificition, you read about the nails, that image is linked to that. If you believe in that event and saw one of those Nails wouldn't you think them to be holy things on some level? Probably.
At least, that's how I look at that particular item of power. I could be wrong and they get power directly from the source and not from the believers. Or the Swords could have power of Faith because Jim Butchers says they do.
I was just thinking about a gun from the Old West Working in the same way. An item of power that has power because enough people believe that it is important.