Enthuware

Are these two statements with bold font conflicting each other?

if thebrowser supports cookies, ... URL encoding is unnecessary.

For robust session tracking, all URLs emitted by a servlet should be run through this method. Otherwise, URL rewriting cannot be used with browsers that doe not support cookies.

No, they are not contradictory. You are ignoring the word "otherwise". It is saying if you do not run the urls through this method, then URL rewriting cannot be used with browsers that dose not support cookies. If you read the first sentence again, which you have not quoted, " The implementation of this method includes the logic to determine whether the session ID needs to be encoded in the URL.", the meaning will be clear.
If the cookies are not supported and if you don't run your urls through this method, you cannot implement URL rewriting.
HTH,
Paul.