Handeman, I mostly agree with everything you've stated, just a few comments.
Is an oscillating mode it can occur in one axis or both axis, and can have a rotational axis as well.
In a single axis oscillation there can still be a glide component in any direction, the oscillation might just be higher on one side than the other. Again in multiple axis oscillation (ie coning) there can still be a horizontal glide component in a direction. Only when adding the rotation to an oscillation can we then start to have the effect negate the possible glide component.
This glide (even very slight) will make the rocket land further from the parachute deployment location 100% off the time at zero wind speed, and approach a 50% closer /50% further as the limit approaches infinity.
If the radial frequency is higher, this glide affect can be negated.
I imagine that overall glide is slight in most parachutes to be negligible, but a parachute with a high radial velocity will decently help negate it.
A lot of people on smaller parachutes have shroud lines to two places on the canopy, with the middle being the location of whatever connection to the rocket, tied with a knot or other hardware. This is not the best option for insuring equidistant shroud lines and non gliding canopies.
Now, after all that, I agree that the effect is probably negligible in a proper constructed parachute. But maybe his other parachute had offset lines and just wants to fly
Oh, and there can be wind for the parachute in the air column
Gusts. They'd of course negate out over averaging, but still.... Just because you're floating down in the air column doesn't mean wind speed doesn't change, your inertia would insure there would be some wind before the parachute speeds up to match
