I was going to stay out of this fight,but it has just gotten too silly.
So;"Can twisted wire replace shielded wire?"
The simple answer is yes.
But there is a big BUT.

In a very quite RF locaiton, like the middle of the woods where there
are no electric/phone/CATV lines, no TVs, no motors, no flourescent
lamps a "twisted pair" can work ery well. Slightly lower losses, but my
experiments in such a RF quite locaiton show no practical or detectable
effects for LF through F (say 50KHz through 30MHz).

If you have any RF noise sources, in many cases this will include your
receiver as many modern recievers have some (to a lot) of RFI
potiential,
you will need to reduce the noise that gets into/onto your signal.

Balanced open wire, AKA "ladder line" is better then twisted pair as
far as
line losses are concerend. But open line is more susceptable to ingress
unless
great care is taken to keep it well away from "anything" that will
cause imbalance.
Sadly the "anything" really means anything. At LF through HF the
effects aren't
all that important.

A trick I learned back in the days of tall towers for VHF an UHF TV
antennas was
to put a 1 twist per foot in the twinlead. This often greatly reduced
ghosting from
very bad to not visible.

So back to the orignal question:
"Can twisted wire replace shielded wire?"
Yes, under the right conditions. But in the real world, at least where
I live, Coax,
or Twinax or Triax, is much better because it reduces any additional
noise I could
pick up as my lead in leaves the antenna and reaches my receiver. I
have used
common twisted "bell" wire when I didn't have coax and if the location
was quite, it
worked great.

The real question is not can twisted wire be used, but how well can you
isolate
twisted or parallel(think lamp cord) from your noise generators. It
can be done,
but coax is a lot easier to keep quite.

I have enough RF noise that I can't reduce, there is no way I want to
add any more
RF crud to my 1uV signals.

Terry