SQL Server replication: can I modify contents of a snapshot?
I've experimented quite extensively with the mentioned situation and it looks like there are different scenarios in which snapshot is re-created: sometimes they involve bulk data being transferred, sometimes they don't. I suppose that the logic on the Publication side is clever enough to see when re-initialization of a subscription will require data being loaded again, and when - not.

Sometimes it brings disaster though, like when you try to re-create a filter, aren't able to and then would have to drop the article and create it again with a filter. The data is actually good on both sides, even if it's not matching the filter on the subscription - well, so what - it will after some updates. The problem is that then the snapshot will be re-generated and subscription marked for re-init. But the table is full of (good) data already and more likely than not you get an error trying to apply the snapshot. 

So then, as in my question, I took all the involved .bcp files and emptied them (with a powershell script as they were many). Deleting them didn't help, because snapshot realizes something's been stolen from it. But empty bulk data files are harmless and then everything goes through, thankfully!

I suppose you could find a scenario when your application would suffer from some data being temporary present that doesn't match the replication filter, but in my case I think everything is working - so far so good.