The BEST solution to this problem appears to be to upgrade to at least .NET 4.6 or later, which will automatically choose strong protocols as well as strong ciphers.
If you can't upgrade to .NET 4.6, the advice of setting
System.Net.ServicePointManager.SecurityProtocol = SecurityProtocolType.Tls11 | SecurityProtocolType.Tls12;
And using the registry settings:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft.NETFramework\v4.0.30319 – SchUseStrongCrypto = DWORD of 1 HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft.NETFramework\v4.0.30319 – SchUseStrongCrypto = DWORD of 1
Results in using something other than TLS 1.0 and a strong cipher.
In my testing, only the setting in the Wow6432Node made any difference, even though my test application was built for Any CPU.