No pictures here, as I said I respect your opinion and I am merely gathering opinions.
So the fact that a patched tube does not have a uniform shape when inflated has not affect on its integrity.
Anyways I have been up since 5am so I am off to bed, day starts same time tomorrow.
OK, here goes. It may be long but stick with me.
Concept 1
When you inflate a tube without a tyre constricting it, the following happens.
The tube inflates and grows bigger and bigger. If you were to measure some ratios, you'd find that it stretches and grows twice as much in girth as in length. It isn't easy to see this because the section is so much smaller than the circumference. However, this happens because of something called hoop stress When you pressurise a cylinder, the stresses in the longitudinal direction are half that of what's called hoop stress, the other direction. I'm sure you can visualise the "hoop".
When the cylinder is a joined at both ends, like a bicycle tube, then it is still a cylinder that adheres to the definition above and that's how we know which way the tube "grows" with inflation. Pump one up and have a look at what happens. You can even do some measurements. It is fun. Now inflate one of those sausage baloons and do some measurements, you'll see the same happens.
The reason you don't see this in a cylinders such as a gas storage tank is because the expansion is minimal - steel resists the expansion very well. That doesn't mean that the stress that the steel "feels" in the two directions don't also conform to the 2:1 ratio. Rubber is softer and because of the nature of how it expands, it expands equally easy no matter which direction you stretch it.
Concept 2.
This mode of expansion is no use to us on bicycle tyres. We can't have tyres which become bigger with inflation. You would have noticed from your experiment above that the circumference alone is so big that you can fit a 35inch wheel into a tube that's inflated to only 10 PSI. Tyres are also made of rubber and also roughly tubular. Inflate them and they will grow? What now? Hold that thought. Enter, High Pressure Hose.
I'm sure you've seen this before. It is a roll of high pressure hose. I'm sure you can spot the solution to inflation. Simply reinforce the hose/tube/tyre with some strong cord and presto!. No more expansion. WRONG!
Remember, we said Hoop Stress is twice that of longitudinal stress. That means that no matter how strong these cords, the hose will become fatter and shorter when it is pressurised. The cords act like a scissor jack and will simply accommodate change in shape. To prevent hoop expansion they will have to be rolled into a very tight helix so that there is no discernible angle between them - perfectly radially would be ideal. To prevent longitudinal expansion, you'll also have to insert a lengwise set of cords. Have a look at the picture above. There's none of that. Just a set of scissor-jack cords.
The secret to the solution lies in the angle of these cords. If you can figure out the exact angle at which the scissor jack expands in such a way to counteract the hoop stress and longitudinal stress at the same time. you'll have a length of hose that neither expands nor shortens when inflated. Remember, I said it acts like a scissor jack, so when it expands, the cords pull the hose in (instead of our bicycle tube that just grows longer and longer). That magic angle is 35.7 degrees. If it was just 45 degrees like we would intuitive choose, then it will shorten under inflation and grow a little fatter. We don't want that, so we choose 35.7 degrees.
Concept 3.
Now that you understand Hoop stress, it is a simply matter of putting some cords in a tyre and pump it. Not! Life is not that simple. Tyres require a bit more finess. Firstly, a bicycle tyres must be fitted by hand and it requires a hard, strong bead to resist sideways forces that want to pull the tyre off the bead. Note that the pull-off force in a tyre is not circumferential, but lateral. That's another story. Anyway. in order to get us poor weaklings to fit the tyre relatively easily, it is made slightly oversized. Yup, to big. However, by clerverly fiddling with the cord angle, the tyres are made to constrict upon inflation. They grow a little bit fatter but a lot shorter. An inflated tyre on a rim is thus smaller in circumference than a non-inflated one. This has bearing on spoke tension too and can be measured. IN other words, not only can't the tube go anywhere, it is also constricted during inflation inside a tyre.
Therefore a tube in a tyre doesn't grow, doesn't stretch the tube and only experiences compressive stress i.e. a force that pushes it against the tyre and attempts to make it thinner and harder. (Rubber becomes hard and loses elasticity when compressed).
Concept 4.
Local strength causes general weakness. This mantra is what's used by engineers to predict where failures in stressed structures will occur. I'll start with an easy example. A ship has a crack in the hull. A mechanic welds a thick piece of metal over the crack - a bit like a patch on a tube. The next crack will grow exactly next to that patch because of the way stress lines are concentrated at the patch. One way around this is to "feather" the piece of metal patch by chamfering the edges s that there is a smooth transition from hull to patch back to hull. We do exactly that with tube but not for the reasons explained in the ship example. That's the reason your Michelin mechanic assumed, but he was wrong. That method of failure only happens when the structure is repeatedly stressed (stretched and relaxed) in the region of the patch. In a tube, that doesn't happen. The tube is inflated, constricted by the tyre and then never again stressed until the next deflation and inflation. Further, the stressing of the tube's rubber happens well within its plastic region of deformation, so there's no damage done by repeated stress either.
The reason why patches are feathered is to prevent lift-off of the patch during handling.
I hope that helps you to rationalise why a patched tube is perfectly safe. Of course, you have to learn how to patch a tube. That's an art worth acquiring and a fine skill to have in your cycling skills arsenal.
BTW, re-purposing your old tube for stringing up some Christmas lights does not negate the tube's pollution footprint. It merely makes you feel better.