It goes even deeper than that, but as others have said in this thread, yes: a processor with a higher clock speed is "faster" than a processor at a lower clock speed, but only at one thing, and that's the number of cycles per second (i.e., the "oscillation").
A 2.16GHz processor processes instructions at a rate of 2,160,000 "cycles" per second.
A 2.0GHz processor processes instructions at a rate of 2,000,000 "cycles" per second.
...but there are many, many, many different factors as to which processor can do a specific task "faster" like DeltaMac said -- the amount of L2/L3 cache the processor has, the type of architecture it has (RISC processors were "faster" than an equally-clocked CISC processor), the number of cores (or "brains") the processor has, etc.
So, now that's great and all, but here's another catch: doing a division operation on one processor may take 22 cycles, while on another processor, that same division operation only takes 17. What if the faster processor takes 22 cycles, and a slower takes 17 cycles? Who is faster then?
So, if you asked me, "Which is faster, a 2.0GHz processor, or a 2.16GHz processor?" then I could not answer that without knowing what types of processors the 2.16 and the 2.0 were. The only way I can answer that question is to say, "The 2.16GHz processor has a higher cycle rate than the 2.0GHz processor," and that's it.
So, in essence, neither of you are right, and both of you are right at the same time. You cannot simply look at the clock speed of a processor and say, "This one is faster than that one."
I'll put my quad-core 2.5GHz Intel Xeons up against your quad-core 3.0GHz Intel Core 2 Quad processors any day of the week and mine will be faster at any task you throw at it (well, maybe with the exception of "counting" from 1 to 1,000,000), because "speed" does not just depend on clock speed, but a whole host of other factors concerning the architecture of the processor as well.