Earlier quoted context omitted.
That's absolutely not true if you also use the registrar for DNS. We transferred a domain away from Network Solutions a few weeks ago, and got bit by the combination of: 1. When you re-point your domain at non-NetSol servers, they momentarily point toward a server that in turn says your A record is their "business profile" default landing page. It takes a few minutes before pointing correctly at your new name server…
If either you, or your old provider do things right, there is no downtime at all. In your case it looks like Network Solutions kinda screwed you over. Here's the correct recipe: a) Tell new registrar about incoming domain transfer, make him already set up nameservers. b) Set the new nameservers for your domain. c) Actually transfer the domain. If either your old provider is nice enough to not shut down your name serv…
People using GoDaddy for both registration and DNS could find themselves in exactly the same predicament, so it makes sense that they'd want to do it carefully.