Stunnel won't work with SSLv3 from some hosts
Solution 1:
Ok, problem was solved... I added this to configuration:
sslVersion = all
options = NO_SSLv2
As far as I understand, error was related to SSLv23. Now all works as expected.
Solution 2:
SSL3_GET_RECORD:wrong version number is the key. It seems that lynx on your CentOS systems isn't using SSLv3.
It'll be easier to check the exact behavior with openssl s_client:
Check what happens with just SSLv3:
openssl s_client -connect server:443 -ssl3
And with just TLS:
openssl s_client -connect server:443 -tls1