my 0.02 (13 years experience working on 'something to do with the Internet')
1 - Typing "jw." will autocomplete to jw.org in google.com. Unfortunately for the WTS typing "jw" autocompletes for 'jw pepper'. Thats why they are making the big deal about the period. https://support.google.com/websearch/answer/106230?hl=en On google.co.uk "jw" autocompletes for "jw3" leading to jw3.org.uk - again "jw." autocompletes for jw.org.
2 - There is a slight nuance if you look closely. Type "jw." (don't hit enter) and it will autocomplete for jw.org and also display the Results Page with jw.org listed first. The second result shown is for jwleaks.org and then jwsurvey.org. Its only when you hit enter you will see jwpepper.com, jwpet.com etc. So every person typing "jw." and then looking down into the Results will be visually exposed to apostate sites. Dangerous this internet thing.
3 - The WTS don't need to and will not have paid Google anything for the above. jw.org is already the number 1 entry on the Results Page (beating jwpepper.com into 2nd place on google.com and jackwills.com on google.co.uk). Note the difference between SERP (Search Engine Results Page) and autocomplete.
4 - The WTS may indeed have had an advisory conversation with Google - you can too - just call them up and ask how to get your site listed - 1-866-2GOOGLE - they will try and sell you ad-space of course, but you can tell everybody you "talked to Google about your site placement". <wink wink>
I would expect in time that "jw" without the period will autocomplete to jw.org on most Google properties - jw.org is an extremely large site with high traffic and thats only going to grow as the WTS funnels more visitors towards it. The speaker at the SAD has been misinformed if he thinks this is a special arrangement with Google - its just the way autocomplete works.
If you are interested in manipulating SERP for payment then take a look at:
http://en.wikipedia.org/wiki/Reputation_management
http://en.wikipedia.org/wiki/Search_engine_optimization
EDIT: Interesting footnote - typing "jehovahs" into Google.com autocompletes for "Jehovah's Witnesses" and places http://en.wikipedia.org/wiki/Jehovah's_Witnesses above jw.org - another reason for the WTS to promote searching for "jw."