What arguments do KJV-only proponents give to support that the 1611 translation is better than say, Greek language Bibles? I have an interlinear Bible, called the Apostolic Bible Polyglot, that presents the New Testament (along with the Old Testament, from the Septuagint) in Greek and English. Of the Complutensian Polyglot, the NT Greek source for the Apostolic Bible Polyglot, Wikipedia says, 


  Theodore Beza's Greek NT Text was used primarily, along with Erasmus' Greek NT Text and with various readings from the Complutensian Greek NT Text to form the Textus Receptus published by the Elzevir Brothers in 1633, and Erasmus' later editions were a secondary source for the King James Version of the New Testament. The Complutensian Polyglot Bible was a tertiary source for the 1611 King James Version.


What arguments do KJV-only proponents give against the authority of Bibles like the ABP that share, and even indirectly lend, source material to the 1611 KJV? What about the authority of the Greek manuscripts that Erasmus originally used for the Textus Receptus?  Do KJV-Onlyists hold at least those manuscripts in high esteem?
You will find the among some KJV-Onlyists the assertion that the 1611 KJV Bible was directly inspired by God.  That cuts away any need for them to explain why the KJV can be considered the infallible word of God while its immediate predecesors should be viewed with scepticism.

For example, Peter Ruckman:


  The text of the A.V. 1611, in Genesis 27, is the inspired infallible
  text, preserved without error.


and:


  The Holy Spirit has thrust Himself into the AV committee of 1611 and
  said, “WRITE…!


and:


  The “truth” is that translations can be given by inspiration.


Now, it should be pointed out that he seems to make some distinction between "inspired" and "given by inspiration":


  What version of the Bible was the inerrant, infallible, inspired
  translation prior to the AV1611?” Answer: Who cares? Ask the people
  that read it. We believe the one we have is infallible and inerrant
  and is “given by inspiration” (not “inspired”).


but it's hard to see how that distinction makes any difference.

The only conclusion that seems possible is that the KJV-Onlyist believes that the earlier manuscripts used by Erasmus, Beza, Stephanus etc. were good, but probably not perfect.  However when the time came to translate those documents into English, the Holy Spirit supernaturally guided the translators to choose the correct words from their available manuscripts, and replace any errant words with inerrant words as the Spirit inspired them.

There is also a view (put forward, for example, by David Stewart) that the many versions that led up to the final KJV translation represent a fulfilment of Ps. 12:6, where God's word is likened to gold refined seven times.  

Personally, I think the claim that the KJV is the result of a supernatural re-inspiration of the translators by the Holy Spirit is an indefensible claim entirely without scriptural warrant.  But if one accepts that as their foundation, it allows them to easily sweep aside questions of which older manuscripts were accurate.  Like Peter Ruckman says, who cares what God's inspired word was before 1611?  Not him.

Citations:


http://www.ruckmanism.org/inspiredornot   
http://www.jesus-is-savior.com/Bible/inspired_or_preserved.htm