Of course woods and varnish have a role as with the overall size of the instrument as well. Horsehair bow vs. synthetic. Type of rosin used, ivory frog vs. plastic/bone frog, type of wood in the bow, etc..etc. The player is probably one of the more important keys. A good player can help a not-so-great instrument sound just a little better.
Citing all of this I think it is nearly impossible to obtain a perfect recording, unless you are Maxim Vengerov or Hogan. Then you are just perfect whether it be an iPhone recording or professional. ;-)