I was wondering if agents ever approach independent publishers with manuscripts, or whether it's solely a big-business domain?
Yes, we absolutely do approach them, but it depends on whether we know they exist and whether we have a relationship with them. I've tried to make contact with more than one small independent I've discovered in a magazine or newsletter, but received no response - I'd love to send things to them, but am not going to do it if I think the approach is unwelcome.
I submit to independents at the same time as large houses, and quite often independents are a better option for the writer, because they'll get more attention on a smaller list (first novelists, in particular, can get lost on large lists - UQP does well with fiction, for example, because it's a relatively small list and they can give individualised attention to the writers). Most of the independents use the larger publishers' distribution channels, and they effectively use in-house or freelance publicists so there's no deficit in terms of publicity for the book. Where they can't really compete is in shelf space within chain bookshops, but sometimes that doesn't matter. It all depends on what the book is. If I think an independent would be a better publisher for it, I'll tell the author that.