regarding your question about "contradiction", I think it would be helpful to remember that the "one additional via" per pin was probably intended to allow the designer to make better power plane connections (more direct connection with two vias, and less inductance on device power pins and decoupling caps, filters, etc). Those type of nets aren't typically routed beyond the fan-out.
The other rule was probably intended to alert the designer if the router is trying too hard to complete a connection. For example, if you have a long two-pin net but the router is trying to use a dozen vias to accomplish it, you would want that route to be flagged.
I've never tried to put multiple fan-out vias on a pad that was going to get routed, but I would assume that the extra fan-out via WILL get counted as one of the routing vias. I could test if for you but I don't have Expedition loaded right now. I would bet a lunch on it, though