I came back from the Grand Central store today with a brand new iPhone 6 because my old one had a small black speck in the very top left part of the screen. It wasn't a dead pixel but they designated it simply as a "foreign object". Very simple switch to a brand new device.
What's great about Apple is that they will gladly replace the phone if it isn't PERFECT. One tiny dead pixel = replacement
Same case here and I went to Apple Store to have my iPhone replaced.
I found instantly that the new unit got the same problem.
They gave me another one but I still found a dead pixel on it.
The third attempt still no luck, a dead pixel in the middle.
They then said that they need to order a new phone for me cause the stocks they got may have the same problem, and I have to wait like 1-2 weeks for a replaced unit.
When I had the iPhone 4, I had problems after problems after problems. And I would really hate to say this but yes, you will end up playing the lottery game. But more than likely, you might be able to get one without a dead pixel.
An iPhone refurb is just as good as a new phone. New shell, new battery, same warranty. It's not like they take returns, wipe them with a baby wipe and rebox them. Any concern about an Apple refurb is... unnecessary.