"This one-time code flow has security advantages..." The statement is absolutely valid while considering one of the most dangerous attack a web application can suffer. It is the Cross Site Request Forgery (CSRF in short).
Before explaining the advantage of one-time code, let me clear the concept of CSRF. CSRF is the number 8 in OWASP list of most dangerous vulnerabilities in 2013. If a web application is vulnerable to CSRF, then it is possible to execute any script for the hacker at the user end, provided the user must be signed in. Basically what happens is the attacker will create urls or POST requests which containing malicious codes, they can be even the JS codes to grab the session cookies of the user and send to the hacker. Now these urls are send to the target user through emails and chats. The POST requests are implemented in his own site by the hacker and the link is given to the victim in the same manner. Since the user is logged in, once he click on the link the hidden scripts will be executed at the user end and he gets hacked.
The only possible prevention method against CSRF is by implementing tokens in each page. Once the user logs into his account, server assigns CSRF tokens to each pages in the web application. Now that each time any links are clicked, the CSRF token is send to the server and server gives permission only if the it accepts that token. What you have to think that a link clicked from e-mail or chat will be having a different CSRF token and hence it prevents this attack.