"The end of Pi?", this can't be mathematically valid, right?

So check out the second answer in this link below (it's kind of long so I just give a short description below):

How can construct pi geometrically | Answerbag

Basically, this guy is saying that physically "Pi Terminates at an exact point". Not that, when we draw a line, we can only ever get closer and closer to the exact value of pi, but we will never reach it. No, he says that since "The smallest possible measurement is the Planck Length", then Pi can theoreticall be drawn to an exact accuracy, since the Planck Length divides distance into the smallest possible length, and the accuracy would only have to lie within one planck length, or something like this. I don't buy this. Is this a valid **mathematical **argument?

Heres where I think its wrong: Just because there is the smallest possible physical distance, that doesn't mean that in "theory", we can't imagine (and even mathematically use and describe) a smaller distance then the Planck Length, right? And since the more "pure" mathematics is more about math theory, his "Planck Length" argument doesn't hold up against the rigor of proper mathematics, correct?

Or am I wrong? Thanks in advance for any assitance.