As wrong as that is, to joe public it's effectively true. It's on the tube map, it goes in a tunnel through the centre of London and interfaces with underground lines at stations that have no other NR presence (e.g. Bond Street). To all intents and purposes of those using it in the core section, it's a tube line. Much moreso than Thameslink or especially London Overground would be.
As far as the DVA is concerned, I think I'd prefer Parnell or Hignett just because pretty much everything uses Julie Berry these days, but there's a good reason for that - hers is the most professional sounding voice. Parnell is fine, but Hignett's announcements I agree aren't quite up to standard, though a lot of that really has to do with how the services she announces have been programmed, rather than the voice actor herself. The LO announcements are mainly so frustrating as they are far too long, repeat information that doesn't need repeating, and so on and so forth. Assuming the 345s are programmed sensibly, any of those three voices would do.