Are inner city areas attracting older residents?

If I had a dollar for every time I was told that older people are downsizing in droves and leaving the suburbs for the inner city, I'd be a much richer person.  This perception has persisted despite the evidence to the contrary.  Every so often an article will appear in a newspaper that perpetuates the myth.  The most recent example appeared in the SMH and used a case study approach to illustrate how the inner suburbs are changing through in-migration of older persons, and how this might continue into the future.  While there's little doubt that the individuals in these articles did make such a move, but is really it a trend?  Let's have a look at the evidence, using inner Sydney as a case study.