I read Terry's work again, the comments and links.

White noise generated with the B-E junction of a high
Ft transistor, B-E junction is a zener.
If you downconvert above 100kHz, that's where white
noise starts, and display it with your soundcard you
"should" get a flat respons.
The methods where right, the spectrum used was too
low.
Add zener noise to your soundcard and you get pink
noise, because at low frequenties the noise behavior
is always pink + the 1/f semiconductor flicker noise.
You can justify it, but that's manmade white noise.
If I was interested in random numbers, I would use
real white noise, real random.
The keyword here is downconvert in KISS concept,
simple as possible.
Semiconductors produce also white noise.
If you can't display white noise, that does not mean
the noise generator produces non.
I would not trust my sound card at all, because with no
input the FFT shows pink noise, ok,at very low level,
but its added to your not anymore random signal.
I have tried Spectran FFT software.
Peaks from noise floor up to 20dB in the range of zero
to hundred hertz.
The computer is full of signals inside, that's not random
compared to white noise.
If you are measuring relative great signals, the little noise
does not improve the S/N ratio so much that you cannot
copy the signal anymore.
But random noise added with little pink noise is no longer
random, how small the error is, especially if the error is only
at a specifiek part of the spectum.
Maybe a professional A/D chip can do the job ?
Unfortunate a spectrum analyzer can show you the white noise,
but cannot make numbers out of it.
To make numbers out of it is the difficulty I think, not to get
white noise.
The analog world and digital world have a " love and hate"
relationship, sometimes they work fine together,
sometimes not.
I don't say the above statements are right, its just how I think
about the experiments at my point of view.