ECG / EEG Amplifier design tricks
The problem with the high pass filter in this application is due to the very slow response time of the filter (because the filter is at such a low frequency).  When the input is overdriven, ( for example, when the patient is defibrillated), the filter takes a really long time to settle, so the signal output is not visible to the doctors, so they don’t know if the patient is still in fibrillation or is dead or is ok. 

Overcoming this response time problem while still providing the correct high pass filtering leads to the different ways of implementing the high pass function that you have noticed. A good solution calls for clever design.