What makes strings sound "sweet"?

I'm not invalidating the importance of the role of the recording engineer. I'm just saying that they almost always do a good job, at least in my experience across a wide variety of classical music. It still remains a stereo system issue. Besides, the point is moot. What can you do? Re-record all your favorite pieces. Try the cables. They aren't smooth or sweet, just real. Even Gidon Kremer sound good.

The problem I have is that it varies from recording to recording. So there's really no way to balance your system to make everything sound good, unless you roll the highs off so much that other instruments start to sound dead.

When I come across a recording with screechy strings, I typically grit my teeth and listen to something else instead.

There is one thing no one mentioned. That is the type of violin and strings used in that recording. That will have a significant effect on what you here (obviously). The recording is part of it, yes, but I can tell you you'll run screaming if I place Dominant's run-of-the-mill strings on my violin versus Pirastro "Olive" Gold strings which are silver/nickel wound over gut and you'll melt in your chair.

The point of my response, while the OP is geared toward the recording, it still failed to recognize the instruments themselves. Some people really just play on crappy strings. It may have been the recording of the century too but it still won't sound sweet.

I think it is due to tone woods and the type of varnish they use and the strings and the bow and the player too.
How to get to Carnege Hall - Practice!

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. ;-)