Reading the question and the comments, there may be a conceptual misunderstanding : the attenuator WILL attenuate any noise presented on its input (even from just a 50 ohm source impedance), to the same extent it attenuates the signal.
However it also generates noise of its own, which may be represented as the noise from a perfect resistor equal to its own output impedance, and this is added at the output to the (attenuated) input signal and noise. So if input and output Z are both 50 ohms, the net result is attenuated signal + marginally increased noise (i.e. NF = attenuation).
But if its output impedance is lower, the added noise is also lower, thus improving the noise voltage as Andy states.
So represent the attenuator as a perfect attenuator (attenuating noise) in series with a Johnson noise voltage source equal to the output impedance. The rest is just applying the formulae.
EDIT: re: updated question.
(1) There is nothing special about 290K except that it's a realistic temperature for the operation of a passive circuit. The reason they chose it is that the article quotes a noise floor ( -174dBm/Hz) which is correct for a specific temperature : yes, 290k.
(2) While any resistance in the attenuator will contribute noise, I realise that it is not a satisfactory explanation as to why you get the same noise out of an attenuator, because (as Andy says) you could make a capacitive attenuator which is not a Johnson noise generator. So we have to look a little deeper, and remember these noise sources are the statistics of the individual electrons that make up the current.
So, let's say we build a (50 ohm in, 50 ohm out) attenuator, and attempt to cheat Johnson by using a capacitive divider. That implies a node within the attenuator which conducts some of the input current to ground. At this node, we have two current paths; a fraction of the current flows to output, the rest to ground. What determines which path an individual electron will take? Essentially, chance. Collectively? Statistics. So this is a noise source.
Or let's just add series capacitance to provide enough attenuation : we thereby avoid dividing the current flow and eliminate the noise source, right? At the cost of reducing the signal current; our statistics now operate with a smaller sample size and consequently greater variance : more noise.
These results are the best you can do, there is no way round them.
Without a schematic I cannot determine if your grounding is correct, i.e. common ground, a common reason for some of the symptoms you describe.
Another point to consider is the liberal (correct) use of electrolytic capacitors and bypass capacitors.
Using a battery-only supply does not guarantee clean power supply rails. Are we sure the battery has adequate reserve available during circuit power up?
Given those conditions are properly met, you might consider the use of a "Supervisory" circuit for your processor.
MCP120/130
• Holds microcontroller in reset until supply voltage reaches stable operating level
• Resets microcontroller during power loss
• Precision monitoring of 3V, 3.3V and 5V systems
• 7 voltage trip points available
• Active low RESET pin
• Open drain output
• Internal pull-up resistor (5 kΩ) for MCP130
• Holds RESET for 350 ms (typical)
• RESET to VCC = 1.0V
• Accuracy of ±125 mV for 5V system
The Microchip Technology Inc. MCP120/130 is a voltage supervisory device designed to keep a microcontroller in reset until the system voltage has reached the proper level and stabilized. It also operates as protection from brown-out conditions when the supply voltage drops below a safe operating level. Both devices are available with a choice of seven different trip voltages and both have open drain outputs. The MCP130 has an internal 5 kΩ pullup resistor. Both devices have active low RESET pins. The MCP120/130 will assert the RESET signal whenever the voltage on the VDD pin is below the trip-point voltage.
They are available in TO-92, SOT-23-2 and 150mil SOIC.
Datasheet: http://www.mouser.com/ds/2/268/11184d-68220.pdf
Very handy little device for $0.60USD, or less!
Best Answer
Chances are that the "mechanism" is capacitive coupling and, of course, the hand can act as quite a good "earth barrier" in these circumstances. But, like you said the hand (as a capacitor) can also slightly slow down a signal on a PCB trace to enough of an extent that the problem is fixed; not because of interference but because the signal edges were slightly slowed down.
Because the hand-to-ground capacitance is going to be in the region of several hundred pF whereas the noise-to-wanted-signal capacitance is only going to be a few pF. Using the hand as a barrier represents a big attenuation to the potential noise.
There is less chance of it being magnetic coupling because the human hand would not have anything like the effect you are seeing.
As for fixes, try using a bit of aluminium foil between likely noise source and victim signal to see if it helps when the aluminium is close to the victim or close to the possible perpetrator. If close to the possible perpetrator then it's likely interference. If close to the victim then there's more chance that adding a small capacitor to ground will slow the signal down enough that it doesn't cause a problem.
You have to be logical about this of course and also try some ferrite shielding to see if that has an effect.