No, you are assuming wrong. What the other Rogues are doing is Mutilate from stealth, Rupture, Mutilate, Slice and Dice, then continue your normal rotation while maintaining Rupture, Slice and Dice and Envenom. There is no double Rupture. You apply a preferably 5 combo point Rupture the moment your initial Rupture is falling off.
You aren't even getting a free Garotte tick unless you are counting in for a possible 0.05 second server lag. We get Rupture rolling one second later compared to you rolling Garotte. And Garotte ticks every 3 seconds instead of every 2 seconds like Rupture. There is no gain anywhere. Opening with Mutilate from stealth deals more damage, generates 2 guaranteed or even 3 combo points on a crit, has a chance to proc Blindside, gives you 2 chances to apply your poison, and don't lose a single Venomous Wounds tick. We spend less energy by making better use of Shadow Focus and lose nothing for it.
This whole back and forth game is getting annoying.
EDIT:
Tiny bit of math before you bring up the pathetic Garotte damage.
Just logged in and compared Garotte's damage to Mutilate. Bear in mind this is just the pure damage from these two abilities and not the other benefits like Mutilate proccing poisons.
Without any crits from either ability:
Garotte's damage was 15525.
Mutilate mainhand and offhand combined was 31565.
Even Mutilate's mainhand strike was beating Garotte.