I hate to break it to you, but you have yet to list anything that would constitute "Digital" noise. I think your ignorance is showing here. Everything from RF interference to a bad power supply are types of ANALOG noise. AND!!! turning your mic preamps up and recording with hotter signals will only AMPLIFY those noises, not mask them.
The example you site, quoted above, will get louder as you record louder. The cell phone interference is analog, and as such happens either before you get to your DAW audio interface or after your interface on your way to the speakers. Turning up the preamp to record hotter also increases these artifacts. Recording with LOWER levels will actually help to get rid of them since you are pushing them down closer to the noise floor of the system.
Anything at the same level or lower than the noise floor of the system gets "swallowed up" by the noise in the system. This is true for analog tape and for digital recorders. The difference is, the noise in digital recorders is 30dB to 40dB lower than that of any analog counterpart. So, recording your levels lower puts your analog noise down into that realm (and if it isn't swallowed up by the system noise it might very well get swallowed up by dither when you master to 16bits). Recording lower also gives you more headroom for digital processing when mixing.
Let me ask you this... if you record as hot as possible, what happens when you EQ something? If you are recording a signal up to -1dB, and then you boost any frequency band using EQ by more than +1dB you are clipping the signal inside the EQ.
Your "sterile digital" recordings are "sterile" because you are recording too hot. No tube preamp is going to help that, no matter how much marketing hype you read. You are getting all this clipping and harmonic distortion within your plugins and throughout your DAW because your level to disk is too hot. That is what creates a "digital" sounding mix.
If you are recording into your DAW trying to get your peaks as close to 0dBFS as possible. That is the EXACT same thing as recording to an analog tape and trying to get your levels to tape up to +20dBVU.
In the end it all comes down to voltage. Equipment designed to operate optimally at +4dBu do just that; they sound "best" when the signal is +4dBu or as close to it as possible. +4dBu on a Protols HD system (192 IO) is at -18dBFS (or -20dBFS if you use the B trim). If you don't believe me, but a volt meter. +4dBu is equal to 1.228 Volts. Test all of your "analog tube" equipment. You'll see that when a signal is coming out at 1.228 Volts, it is showing 0dB on the VU meter of the tube gear. When you send a 1.228 Volt signal into protools HD (192 IO) it shows up at -18dBFS.
When you are recording as hot as possible you are trying to push upwards of 9 volts (with peaks way above that) out of a mic preamp that is designed to operate down around 1.228 Volts. And you are pushing that 9 volt signal into a line input and A/D that is designed to be linear at or near 1.228 Volts. EVERYTHING about the mic preamps, line amps and converter go "out of spec" when driving the signal that hard. The frequency response is no longer linear and the harmonic distortion increases dramatically, yielding a "sterile" and unpleasant sound. It's compounding. The preamp adds harmonic distortions trying to output such a hot signal...the line input adds harmonic distortion trying to receive that hot a signal, your plugins will potentially add distortion (boosting an EQ freq for example) and then your D/A will add distortion to it because of Intersample peaks... and your line output will add yet more harmonic distortion trying to output a signal that hot and most likely the input of your power amp or speaker system will also add harmonic distortion since the signal is so hot as well.