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eg
"Site X" links to "Unique site name" then "Site X" with a lower PR ranks higher for that Unique site name.
Would this suggest I have a penalty for things like this to be happening?
I have many other links coming in with my site name in the link.
That written, the circumstances that you describe often happen due to a keyphrase penalty. If you're penalised for that phrase and they're not, then they might well outrank you even though you have better links, title, body text etc.
Adding links such as Search Engine [google.com] or Webmaster [webmasterworld.com] add credibility, but those links don't in themselves make you higher profile than the sites you link to.
I don't think he meant it would cause you to rank higher than them in the SERPs
He may not have meant that but this is what often happens. I've seen PR3 page on a big news site (with a home PR of 8) link to a PR5 site using the PR5 site's trademark and URL and suddenly the PR3 page ranks higher for that trademark term than "trademark.com" which is a PR5.