This calls for. . . . Grammar!
I'm not picking on you, but that's what it boils down to, "how is the sentence structured?".
"You may re-roll all of the dice on a single test that did not score a hit."
Do dice score hits, or do tests score hits?
Well, the great book says:
Unlike other games, when you roll the dice in Shadowrun, you do not add them together. Instead, you compare each individual to the standard target number of 5. This target number never changes. Each die that is equal to or greater than 5 is considered a hit. In other words, any die that rolls a 5 or 6 is a hit. The more dice that score hits, the better the result. Players should count the number of hits they score on each test and tell the gamemaster.
So the dice score hits. Regardless of the number of hits on the test, you spend edge and re-roll those dice that did not score a hit to get more hits on the test.
Consider the following examples:
Sammie the Samurai rolls a DP of 10 dice, scoring 2 hits, and rolling 6 ones.
Sammie could do any of the following to improve her luck:
* Spend edge to roll her Edge Dice (let's say it's 3), with the rule of 6 for those dice. This gives her an average of slightly more than 1 extra hit. And she still glitches.
* Spend edge to negate the glitch.
* Spend edge to re-roll all 8 dice that missed, with an average of over 2 hits AND negating the glitch unless she manages to roll 5+ ones again.
Here, it looks like you're right, that first option looks pretty weak.
So what about the following:
Sammie the Samurai rolls DP 6, threshold 4, gets 3 hits, no glitch. She only needs 1 more hit to succeed at the test, so which is better now?
* Spend edge to roll Edge Dice (3 again),
with the rule of 6 for those dice.
* Spend edge to re-roll the 3 dice that missed, no rule of six.
If anything, the re-roll dice that didn't hit option really messes with the "negate a glitch or critical glitch" effect.
For those wanting to look at the book, all uses of edge presented came from the section
Spending Edge, Page 74,
SR4A.