k-anonymity is often only applied to "pseudoidentifiers", if you have the original dataset it'd be trivial to reverse k-anonymity applied that way. For example someone's blood pressure isn't considered an identifying variable, and would not need to be anonymised (should not too, to keep data utility high), however this would make linking against the original dataset trivial.
You are right, time series data like BPM over time does not lend itself to anonymization nicely, the provider most likely will have to ask the user organizations what kind of measures (features) they need and return an average (if that's what the receiving organisation was after) that itself can be k-anonymized.
Averaged time series are very different than individual ones.
This is a deep problem; it's basically unavoidable in e.g. medical research - the very factors you want to study may well be potentially identifying. The only way to address this is to balance the potential utility of the research against the potential impact of the information.
