I just tranferred 10 domains away from Network Solutions without any problems at all and with no attempt from them to charge me anything.
They took between 3 and 10 days to complete, seemingly at random, but there were no issues.
The only time you can be guaranteed of an issue is if your email contact information in your Whois record is incomplete or inaccurate.
As for NSI selling your info, I doubt they have ever done that. It's easy enough to harvest your info with tools like "dig" from the whois servers that no one is going to pay for it anyway...