How much data can I encrypt with AES before I need to change the key in CBC mode?
The $1/2^{32}$ is an arbitrary figure, based upon one particular value for what counts as an acceptable risk.

You need to decide what is an acceptable risk.  If you think that a $1/2^{32}$ probability of failure is an acceptable risk, then this calculation is relevant to you.  If you think it isn't, then decide what you think is an acceptable risk and re-do the calculation based upon the number you think fits your particular situation.

Keep in mind a $1/2^{32}$ probability of failure is pretty darn small -- in many settings, it may be acceptable.  It's far more likely that the next time you'll get into a car, you'll end up in a car accident: the probability of that is probably much higher than $1/2^{32}$.
Also keep in mind that life is about risk: you can never completely eliminate all risk from your life.  So, decide what is an acceptable risk, then you based upon that you can decide how much data you can encrypt under a single key, using a calculation similar to that one shown here.