I don't see why a GM would be unable to say (within the rules) that, of your zero dice, more than half of them (51% or more of zero) came up 1's. That's the only relevant point for judging whether a glitch happens. Successes matter in number, 1's matter in percentage.
If more than half the dice you rolled show a one, then you’ve got problems. This is called a glitch.
There may be circumstances where a player rolls a glitch and also does not achieve a single hit. This is called a critical glitch, and this is where the drek hits the fan.
Then again, I'm not exactly math-focused.
The problem here is that 0 is a weird and special number. In
most cases, if you have 51% (or any percentage over 50%) of the dice coming up 1, that's "over half" of the dice. So if you had 0 dice, then 51% would be 0, so it'd be "over half" for that reasoning. But the 51% rule is a shortcut, and doesn't apply in the case of 0. After all, what percentage of dice came up 1? You have 0 1's and 0 total dice, so the percentage is 0/0 (*100%). 0/0 is indeterminate; 51% is "correct", but so is 12%, or 4242%. Because 4242% of 0 is
also 0. And, crucially, 50% - half - is also possible. Since 0 is half of 0, 0 isn't
over half of 0 (even if 51% of 0 is also 0), so it's not enough. So you can't use this line of reasoning for 0, because 0 is weird.
You can, however, work reversely from the other side. The rule states that "over half" of the dice needs to be one. So whatever number of dice is half, you need to have a number that is bigger then that. Since dice come in whole units, you need the first whole number that isn't half the dice pool itself.
50% of 0 is 0, so you need one more dice then that, so you'd need at least 1.
Of course, that's the mathy, strictly rules-wise interpretation; I already stated that I wouldn't mind a houserule like that. But within the rules, as you stated, your reasoning isn't correct.