Andy Wade wrote:

We've done this one
often enough Tony, both here and on uk.tech.digital-tv. If you connect
a coax feeder to a symmetrical aerial (such as the centre-fed dipole of
a typical TV aerial) without using any form of balun then the outer of
the feeder becomes part of the aerial. If you're transmitting, the
outer of the coax will be 'RF-hot' and will radiate, quite possibly
causing EMC problems to low-level parts of the transmitting equipment as
well as safety concerns if high RF power is involved. When receiving,
unwanted signals picked up on this hot feeder will find their way into
the receiver, however perfect the screening of the coax itself.

I don't think that is actually correct.
It is as equally valid to say that the coax outer 'grounds' one limb of
the dipole at its feed end, and it becomes a 'reflector' boosting the
signal into the other half. Ie. the 'balanced' nature of the antenna is
a myth. It doesn't care what the potential is of any limb: what it cares
about is the difference. It can be 'earthed' at any pint.

Baluns are generally valid on unscreened unearthed transmission lines.
Like twisted pair.