Shouldn't that be only those who believe?

This just struck me as a bit off.  Maybe I am just being picky but here is what I thought when I read this.

1 Timothy 4:10(NKJV)

For to this end we both labor and suffer reproach, because we trust in the living God, who is the Savior of all men, especially of those who believe. 

"savior of all men…especially those who believe".

Seems to me that technically Jesus is the savior only to those who believe.  Those who reject Jesus and choose not to believe are not saved so Jesus isn't their savior. 

Why do I point this out?  I think it is because there is a bit of ambiguity in the sentence in the way it is worded in my opinion.  I think it is ambiguity like that that leads some to believe things like "in the end Jesus let's everybody in to Heaven if they have been good", etc.

Don't mean to be picky but it is what God let me to write about today.  :)