It can't hurt to clean it, but I'll admit that I kinda pulled that beerstone comment out of thin air when racking my brain for an example of something unintended that might be dissolving into your wort during the boil.
Since beerstone tends to build up rather than dissolve into wort, on further reflection I'm skeptical that is actually the cause. Perhaps Martin or someone with a better chemistry background could weigh in on whether beerstone (or any other kind of buildup in your kettle) could possibly contribute to an increase in pH during the boil?
Looking back to why the boil pH is expected to drop, this is from Braukaiser:
During boiling the pH drops by about 0.1 – 0.2 pH units from 5.3 – 5.5 pH to about 5.2 – 5.3 pH. This may be due to the addition of bitter acids from the hops, formation of acidic Maillard products, precipitation of alkaline phosphates or the reaction of polypeptides with calcium, liberating protons [Briggs, 2004].
Note that there are several things going on here. I haven't ever seen this discussed, but based on the underlying mechanisms is seems possible that depending on when you're taking your post-boil pH measurement (and what has or has not precipitated out of solution), you could end up with different results.
I'm still perplexed as to how something like that could increase from a 5.3 pH reading pre-boil to a 5.6pH reading post-boil. It still seems to me that there's a simpler explanation, but I'm out of ideas.