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
2. Many large caching nameservers don't obey TTL; our SOA's TTL was 7200, or 3 hours, but we saw servers at RCN, BellSouth and Cox serving our old SOA nearly 24 hours later.
Together, that means that for 24 hours, some people got this lovely page: http://www.vttcorp.com/ instead of our 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 server as soon as he receives the transfer request (which won't benefit him in any way, because he is just helping an already leaving customer) or you follow the recipe from above, you will have zero downtime.
This wasn't even a registrar transfer, just a DNS repoint from NetSol to Route 53. Amazon was all set up before the transfer; it was NetSol's screwup (which is probably some ancient set of CGI scripts) that caused the problem, and there was no way we could have avoided it even if we had known exactly what would occur - NetSol controlled both (a) the registry data telling the root servers where to find our SOA, and (b) the name server that the old SOA pointed to.
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.
I was actually unaware that people used their registrar as their DNS provider. I've personally only used GoDaddy to purchase domains and couldn't for a second thing anyone would want to use them for something as important as DNS.
Other people have mentioned having to move Email as well, but I don't understand why people don't use Google Apps which is free and stops you from having to migrate your email all over the place when you switch hosts.
The person I replied to specified "major sites". How many major sites do you know that use GoDaddy to host their DNS?
But if you're transferring web and email hosting, as I am, it takes a lot more logistical work.
The domains leaving are just the leading indicator. If they're going away, there's plenty of reason to believe that other customers, that will hurt them more, are working on the issue.
