Should non-banking institutions be allowed to provide banking services?

Is "please explain" the heading for a couple of homework assignments?

In many countries, providing banking services would ipso facto make
the institution a bank.  It is a matter of how the country's banking
law defines what is a banking service.  If a service provided did not
fall in this category, then in that country it would not be a "banking
service"  - although in other countries that service might be defined
as such.

At this distance, the question is one of semantics.

The q probably, in an Australian context, means should big insurers
like AMP be allowed to provide banking services - which they do, of
course, by setting up or buying regulated banks.  Australia, being a
small market, has a constant problem trying to retain enough
competition and not let a few players get too powerful.

Jago, 
you may be right, and we seem to have more in common than worrying
about Brian's diet (I'm more worried about his daughter's getting hung
on junk food).  I remember back 35 years ago, when it was impressing
that AMP was said to have A$ 3 million that that it had to invest
every day.
Back to the question:  from my way of thinking, buying a bank is
different from being allowed to provide banking services as a
non-banking institution, but the questioner can clarify.
Cheers, Myoarin