There are several fundamental facts that have been missed in your assumptions.
Quote:
| Surely the fact that he is a google customer has to have something to do with his jumped up page rank? |
It absolutely doesn't!
Google states that AdWords has no effect on Organic search.
It is a different bot and technology that does the spidering for AdWords. That is Google Media partners bot.
Page rank may appear to "jump" because you are probably looking at the Toolbar PR which is not accurate and is historical data only updated every few months and is one of the most mis understood things newbie SEOs look at. Its a waste of time in short!
Quote:
| Google surely has to recognise the link for it to take any page rank value from it. This site has no links recognised by google. 0. |
The link: command in Google is not accurate. Further more there is no direct correlation between any other search engines links or the proportion of which it decides to show.
If a page has a link to you and its indexed in Google then Google knows about it. It just doesn't show users the amount of links it knows about to prevent back engineering of the algorith. It is a random value that it shows. Do not use Googel Link: command for checking your back links.
The Google search page is blocked from Google by its self in the robots.txt file. This prevents any SERPs leaking PR, so any page where Adwords are displayed they can't be considered as links and they are in Iframes on external sites so again, AdWords can't possible influence rankings.
I will say this loud an clear.
ADWORDS HAS NOTHING AT ALL TO DO WITH GOOGLE ORGANIC SEARCH.
ORGANIC SEARCH CAN'T BE INFLUENCED DIRECTLY BY ADWORDS OR ANY OTHER PPC PLATFORM.