I don't really doubt that you're right. Most everything I read on the subject agrees with or is consistant with what you're saying. But the idea is still very confusing to me, so I appreciate your explanations. Let me try to make my troubles more clear.
So far as I understand it, a Planck time is a minimum because that's the time it takes the fastest possible thing to pass through the minimum possible length. If something were going 99% the speed of light, or 75% or any percentage other than 100%, 50%, 25%, 12.5% etc. then it would travel through the Planck length in a non-whole number of Planck times. So something traveling at 75% the speed of light would travel through the Planck length at 1.5 Planck times. Maybe we can't measure this. That's fine. But say something were to travel at a constant velocity through two Planck lengths in three Planck times. Wouldn't it just follow that it went through each Planck length in 1.5 Planck times? It may be that we can't measure anything with precision greater than whole numbers of Planck times, but in this scenario it wouldn't follow from that that time is discontinuous.
Mathematically speaking, you can say "in average it travelled for 1 Planck length in 1.5 Planck time". But physically speaking, it doesn't mean anything. Quantum mechanics works with wavefunction. Objects don't have an absolutely precise position. To know where the object is, you need to interact with it. To interact with it, you need something to happen. Due to Heinsenberg's Uncertainity Principle (even if you consider it as a "certainity principle" as Eliezer does), you just can't locate something more precisely in space than a Planck... (read more)