I've seen the pics of those who have CTB'd with it laying down, but The PPH says never to do that with inert gas (not just helium).
Which edition(s) of PPH do mention body position? I couldn't find any related considerations in the editions I have.
I always thought it was because in a chair, gravity would be working with the exhaled CO2 so it would go down & out of the bag, and making it less likely that air would get into it.
That could make sense if we exhaled pure or somewhat concentrated CO₂. However, in the air we exhale it's blended with other lighter gases, including very light water vapours, so the actual density of the mix is much less than that of pure or concentrated CO₂. A possible composition of exhaled gases can be
75% N₂ + 15% O₂ + 5% H₂O + 4% CO₂ + 1% Ar
See
Composition of Air.
In such a mixture, the average molar mass is
(75% * 28.0 g/mol + 15% * 32.0 g/mol + 5% * 18.0 g/mol + 4% * 44.0 g/mol + 1% * 40.0 g/mol) / 100% ≈ 28.9 g/mol
Blending of gases due to thermal molecular movement and currents prevents stratification of gases by their molar mass within small ranges of altitude.
Why don't the gases in the atmosphere separate out according to mass?
The temperature of exhaled air commonly varies between 31 °C and 35 °C - see
tesble.com
The density of ideal gas is
ρ = M * p / (R * T)
where M is the molar mass, p is the pressure the gas, R is the universal gas constant, T is the absolute temperature of the gas.
If ρ₁ is the density of nitrogen at 20.0 °C and ρ₂ is the density of the exhaled gas composition mentioned above at 35.0 °C and the same pressure, then ρ₁ / ρ₂ can be roughly estimated as
( 28.0 g/mol * p / (R * (273.15 + 20.0) °K) ) / ( 28.9 g/mol * p / (R * (273.15 + 35.0) °K) ) = (28.0 g/mol / 293.15 °K) / (28.9 g/mol / 308.15 °K) ≈ 1.02
which means ρ₁ > ρ₂ (colder dry nitrogen is slightly denser than warmer moist exhaled air).
When we replace oxygen and argon with nitrogen in our lungs, the composition of the exhaled air could change to something like this
85% N₂ + 6% O₂ + 5% H₂O + 4% CO₂ having the average molar mass of ~28.4 g/mol - less than before.
Here we could reduce the absolute humidity to 2% (replacing it with nitrogen, resulting in 88% N₂) and the temperature to 31 °C and still get a less dense composition than dry N₂ at 20 °C:
(28.0 g/mol / 293.15 °K) / (28.7 g/mol / 304.15 °K) ≈ 1.01 > 1