The invetor's slides say that the only time the analogy breaks down is with ungrounded capacitors, though its unclear to me what exactly that means (I don't really feel like thinking too hard about it). See slide 17 http://www-control.eng.cam.ac.uk/~mcs/lecture_j.pdf

There are actually a few different analogies you can make between electrical/mechanical devices. See the top table "Key Concept: Analogous Quantities". This is part of the reason why I don't feel like thinking too hard about what the inventor means when he says the analogy "breaks down" with ungrounded capacitors. http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Analogs/E...

The inventor has created a "new analogy" where the inerter is a capacitor. I read your post as saying the old analogies don't work. Is that correct?