You're not matching the wire to the radio. You're matching the wire to
the coaxial cable. It makes a huge difference.

But still rarely enough to improve the actual s/n ratio. But
in my original post, I was implying the use of the random
direct with no coax used. Unless there is a reason to remote
the feedpoint, IE: to escape a noisy house, there is little
need to use the coax feed. But even with the coax feed,
the chances of coax loss reducing the s/n level on HF is pretty
rare for a decent radio. But of course, this will depend on the
coax used also. Most of mine is 213, which is fairly low loss,
even with a mismatch. rg-58 would not fare quite as well
on the upper bands, although I still doubt it would lose s/n unless
super long, or old, etc..
With my IC-706mk2g, and my multiple paralleled dipoles,
there is no HF frequency where it helps my s/n ratio to use
matching from the antenna to the coax, or to use my tuner.
Even on 10m, I have plenty of background noise present
when I have the antenna connected.
The only band that is improved using a tuner, is 160m.
In that case, the tuner does act to reduce MW strength to
the radio, which reduces images across 160m.
Sure, using matching will often boost the level you see to the
radio. But as long as you had background noise present
with no signal, the noise increases at the same level as the
desired signals. There is no change in s/n ratio. The meter
is just pumped up...

In this case..
I've been using the Palomar MLB with 82ft of random wire over my house with
a dedicated ground on my R-75 for a couple years now. The MLB makes a
dramatic difference in the noise level while increasing the signal strength
anywhere on the SW spectrum.

I don't know what a "MLB" is... A tuner I assume? Or maybe a
preselector?
This is unrelated to the need for impedance matching a random wire to
a coax feed.
In your case, you are either cleaning up a radio with a preselector, or
you
are using some method that provides better decoupling of the feedline.

A ground in itself means nada. Ground is a noise source actually.
But using ground as the shield connection to a coax fed random wire
can improve decoupling of the feedline.
*This* is what is lowering noise, *NOT* the improved match. Or at
least,
as far as s/n ratio on HF is concerned. If using matching actually
improves
the s/n ratio, either #1, the radio is half dead, or very cheap, or #2,
the coax
is super lossy, long length, etc... But it would have to be some
*really* dead
coax on HF. The lower the freq, the less the loss per foot. On the
lower
HF bands, the loss of coax is very low. Approaching ladder line
standards
nearly... You can have a real high SWR, and it ain't gonna kill you.
Impedance matching should *never* be confused with decoupling
the antenna from the feedline. Totally unrelated. You can have a high
SWR,
and have real good decoupling, or visa versa. Or backwards... Again the

two are totally unrelated. It's the *decoupling* of the feedline that
is what
actually benefits most SWL'ers. Not the improved match. The improved
match is overkill in 95% of the cases. Not to say it can't be used for
the
max transfer of power, but just saying it's almost never actually
neccessary
for good reception on a decent radio.

Seems like a lot of people are missing out on
some good dx and a generally more pleasant to listen to radio because they
have not tried this minor purchase.

I'm not one of them. I use only balanced wire antennas. Mostly dipoles.

But also a large yagi on the upper HF bands. I can hear stuff on that
beam,
many people would likely drool over, if they are using just random
wires.
To me, a random wire is a generally poor design, and something I'd
only use as a last resort. Not saying they aren't quite usable for
general
SWL use, but they can be improved on fer sure... Just a balanced dipole

is a big improvement in general over a random wire in general
operation,
ease of decoupling, etc... And as a bonus, you don't need a ground
connection for proper operation. Anywhere. Antenna, feedline, or radio.

All verticals I use, have ground radials, etc, and are also "complete"
antennas.

MK