(I used to work on Google's PageSpeed Service, and if it had had the same bug I think we would have been in the same situation as CF is now.)
Sure it can. But leaking PII from the thing you're parsing and leaking PII from any other random request isn't the same thing.
I understand the performance implications (and the added effort) of sandboxing the parser, but I'm arguing for it anyway. The mere presence of a man-in-the-middle decrypting HTTPS and pooling cleartext data from many disparate services in a single memory space is already questionable (something for Cloudflare customers - and not Cloudflare itself - to think about) but adding risky features into the mix shouldn't be done without as much isolation as possible.
Let's face it: parsers are about the most likely place for this sort of leakage to happen...
It's definitely possible to fix this (new sandbox per request, cache is fragmented by something outside of sandbox control) but I'm not sure the service would make sense economically.