That means that they believe that God has reneged on his promise. I believe that God guided the preparation of the KJV; any other position is a position of unbelief a one level or another. The 'modern' translations are part of an incremental attack on God's word, and their acceptance is evidential of the prophecied falling away.
Both cannot be right; if the modern translations are correct then there was a long period where the world was without God's word. Do you believe that?
Does the fact that God has preserved His word imply that a particular translation is perfect (absolutely no errors), or, simply inspired (subject to human interpretation fault)? What side of this issue do the KJVist's take?
If you read both sides of the argument, you will see two mechanisms proposed for the means God used to preserve His word. Both sides claim that the text has been preserved. The KJV-Only folks have claimed that the KJV is a perfect translation based upon the perfect manuscipts - the TR. Those of us who do not hold this position propose another mechanism: Using the early persecution and dispersion of the church, God distributed the copies of the autographs rapidly over a wide geographical area. No one group ever controlled all the copies. The second part of this argument is the vast number of copies, translations, and and quotations by early belivers. This provides what those of us in science call 'oversampling'. Using the terms of signal processing, oversampling increases the signal to noise ratio. When compared to all other documents of antiquity, the purity of the Scriptures is vastly superior to any other document. It isn't even close.
The KJV-Only school likes to charge the Alexandrians with the heresy of gnosticism and claim that it has corrupted the oldest complete manuscripts. This ignores the influence of Arian heresies in the West. Indeed, the Alexandrian bishop, Athanasius, led the charge against Arianism.