(Not the GP) Yes, when done right, but it's iffy.

For example, the article includes URLs like "/people/123". The security of having a leading slash in these depends on API base URL.

"https://api.hotstartup.com/v1" – safe

"https://api.hotstartup.com" – unsafe with ".evil.com/people/123"

I wouldn't really call this particular scenario a security issue, but allowing such things is a bad habit that will eventually bite. It's like not HTML-encoding values like usernames that you "know" are safe (but you know are not HTML-encoded).