Does using edge increase your chance for a glitch? Options

[Feshy]

The rule for including edge in a roll is that if the roll is a six, you re-roll that die, but still count a hit for that die.

The rule for a Glitch is that if half or more of the dice rolled are ones, it's a glitch.

Okay, let's say that with edge, I roll six dice. The result is as follows:

1,1,3,4,6,6

Admittedly, an unlikely roll. So far, so good. 2 hits, and it's not a glitch. The trouble is, I have to now reroll those two 6's, (but remember that they are hits.) When I do, the dice on the table look like this:

1,1,3,4,X,X, +2 hits.

The thing is, if even one of those two X's are a one, the test becomes a glitch -- this is because re-rolling the sixes doesn't add any extra dice to the check, it just adds (potential) hits. This, I assume, is why the book says to re-roll the dice, and not roll new ones or something. I've thus added a possibility of a glitch that did not exist for non exploding dice.

Is this interpretation correct? Or am I just being asinine? I suspect the later, but I wondered if others had any thoughts along these lines.