Electronic – Why does the X-box 360 controller battery pack have an integrated breaker contact

Connecting cells in parallel is common practise with professional battery pack manufacturers, so there is nothing wrong with it. What pros do is they assemble packs from cells out of the same box (same shipment, same lot), having very tight tolerances. This way, you even get packs with serially connected cells (eg. 3s1p) where the cell voltages stay closely matched over the lifetime of the pack (several years) - without balancing of course. This is quite a considerable achievement, you can calculate yourself how much self discharge difference the cells can have in order not to have significant unbalancing.

Your case is much simpler (1s2p) so I guess you are using low quality cells. The above is only valid for top quality cells (Panasonic, Samsung etc), a lot of "noname" cells like used in aftermarket camera batteries are just crap. Which cells are you using?

Ok, after some additional research I think found some useful information from other manufacturers. I will just quote some points of interest.

From Technical Brochure LTC Batteries

Depending on mechanical cell design and system properties, there is a certain dependence of available capacity on cell orientation during discharge. The effect is caused by the tendency of the electrolyte to move towards the void and inactive space of the battery if the orientation deviates from the preferred direction. The capillary effect of the cathode and separator pores acts against this tendency. As a result, the orientation effect is smaller for thin cathodes than it is for thick ones and is not even observable when discharge currents are very low or when batteries are moved during discharge [...]
At the high current end, available capacity of big cells (C, D, DD) is affected if the batteries are discharged upside down. Therefore this orientation should be avoided if possible.

From Handbook Primary Lithium Cylindrical Cells - VARTA

Under upside down installation, the capacity of smaller size (1/2 AA, AA) is less affected whether discharge current is high, nominal or low. However, the capacity of bigger size (C, D) especially at higher discharge current is affected. Under upside down installation, the lithium and cathode is located in a fixed area whereas the electrolyte falls to the bottom in this case. At the top of the cell there is a space leaving an area of the anode and cathode, not covered by the electrolyte. Bigger size cells have a bigger empty space, so the capacity decrease in upside down installation is higher than in cells of smaller size. (About 20~40% of its capacity at same higher discharge current.)

While we are not "at the high current end" and are using a AA cell, the measurements from above confirm that "upside down" is the worst orientation.

So orientation does absolutely matter when using Lithium-Thionyl-Chloride cells. Learning never stops...