Stunnel won't work with SSLv3 from some hosts

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.

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