Fixing meta title issue please?

Hey guys, with my new WP theme I have been running into a problem with the meta title, using yoast or all in one seo the title changes are not reflecting in the page source view. I had hired a WP coder to fix the problem, it was working but now doesn't and he's "looking into it" but I would like to understand a few things with your help please?

First, my research on the net is confusing, one source mentioned:
The Title Tag

Although the title tag appears in the head block of the page, it isn’t actually a meta tag. What’s the difference? The title tag is a required page “element” according to the W3C. Meta tags are optional page descriptors.

Is that accurate that when I look in the page source here the title I am seeing is NOT a meta title?
http://imgur.com/FFyggeu

 

Search engines are increasingly choosing the title for a page based on the contextual relationship of the page and the search query, rather than using a static title.

The advice for some time from the SEO industry is to ignore meta data, the search engines do!

 

You are the only person to say this but still doesn't answer the question I am seeking.