So, I once had a requirement to prove that a system installed subsea would meet EMI requirements. Including radiated. (seriously). Here is my write-up for that - I would assume that while the Reddit guy is partially correct (interface impedance), there is also something to be said for the energy absorption of the oil (although I agree - that is probably pretty low in this particular instance)...
Not a real proof, I'll admit, but...
Shielding Effectiveness of Sea Water
According to  and , the shielding effectiveness of a shielding mechanism is defined as:
P1 = Incident Electromagnetic Power
P2 = Transmitted power with shielding in place
R = Reflection loss
A = Absorption loss
C = correction term for re-reflection within the metal surfaces
Furthermore, according to , the correction term (C) is usually of small magnitude and is ignored when the absorption loss is greater than about 10dB.
According to , the reflection loss for plane waves is as follows:
And absorption loss is:
µ = Permeability of the material
g = Conductivity of the material
µ0 = Permeability of free space (4πx10-7 h/m)
gcu = Conductivity of Copper (5.8x107 S/m)
µr = Permeability relative to Copper
gr = Conductivity relative to Copper
f = Frequency in Hz
d = Thickness of material in meters
According to , the properties of sea water are as follows:
Combining these values, we find that one meter of sea water has a shielding effectiveness of approximately 125dB at 1Hz, dipping to 101dB at approximately 50kHz, and then increases log-linearly to over 500dB at 1GHz. This curve is shown in figure 1, below. Changing the distance between the noise source and the receiver effects only the slope of the absorption curve – at 10m distance, the knee of the curve moves to 0.1MHz, and this trend continues as depth increases.
As most EMI screen rooms afford 100 dB shielding, and do an effective job at blocking outside radiation, it seems appropriate to consider the system to be contained within a very good Faraday cage.
 MIL-HDBK-1195, Military Handbook, Radio Frequency Shielded Enclosures, September, 1988
 Omer Tolga Inan, Naval Technological Innovations of World War II, March, 2004
Yes, it seems correct that the epsilon of oil is changing everything about the line impedances, etc; Then, maybe the best solution is to run a simulation of redesigning such a circuit optimized for the new epsilon and see the differences. As a reduction, only the impedance of the transmission/ reception wifi may be considered but I wouldn't be to surprised to find out that all the on- board line transmissions are affected. As a first guess, increasing epsilon would cause decreasing the size of the board - that's interesting.
And also, cooking oil is known to have a relative low resistivity (it has got some ions an water in it) - which is certainly increasing electric and electromagnetic losses. This is a known problem - only silicon and transformer oil has good dielectric properties, having very high resistivity, temperature resistance and high breaking voltage.
I'm no expert, but this is an interesting question. Seems like one should be able to find the attentuation values for oil (BTW, what kind of oil is it?) somewhere, then that would answer half of the question.
Also - correct me if I'm wrong, but wouldn't the "air bubble" idea just be moving the mismatched-impedance boundary out farther, i.e. it would still have its effect (whatever that may be) at distances beyond it?
It's an easy experiment. Measure signal strength with the device in air. Then put the device in a sealable plastic bag, and measure signal strength again. Then submerge the bag in oil (thus preserving the air interface for the antenna) and measure. Finally, take the device out of the bag and submerge it.
I suspect that only the un-bagged, submerged case would show a drop in signal strength, because I think the antenna mismatch theory is spot on. Waves passing through a dielectric interface will refract, but not necessarily attenuate, but an impedance mismatch would cause a reflection.
- I didn't take any measurements by the first experiment, since it was just a "does it work at all" test.
But, today I redid the test, this time recording the wifi-strength using the method in the Electric Imp ide doing just that: imp.rssi() ( http://electricimp.com/docs/api/imp/rssi/ )
Here is a graph of the data - There is roughly a drop in signal strength of 10 dBm when the imp is dipped in oil. http://i.imgur.com/Bqm2P3w.jpg
To counter any errors from changing the position of the imp in the room influencing the wifi-strength, i had the imp hanging in a fixed position, and lifted the cup of oil up around it.
Another possible error/uncertainty in this is, that the antenna of the imp is hidden in the plastic container. Most likely the antenna does not get in direct contact with oil. There is most likely at least 1 mm of air/plastic between the antenna and the oil.