The offending box had been flattened to take up less space in the bin. The act of tipping the bin up had caused it to fall "trap door like" across the mouth of the bin thus jamming the items below it in said bin. Ironically, if the objects below the obstruction (or above it once the bin was inverted) had been heavier then they would have forced the blockage out of the way. Unfortunately all of the heavier objects tend to end up in the blue bin, the brown bin, the compost bin or in the paper recycling bag. None of which are suitable for cardboard.
In fact cardboard is about the only thing that we are allowed to put in the grey bin, well that and light bulbs. However, as my house is fully equipped with low energy long life tree friendly bulbs (that take 15 minutes to warm up and are **** all use when they do) that never ever break my grey bin is almost exclusively for cardboard and nappies (we tried the biodegradable ones but they leak. Sorry).
Any road up, back to the OP. A quick inspection followed by a bit of a jiggle freed up the blockage allowing for an unobstructed discharge should they have attempted it again. However, as they had already carried out their obligation of attempting to empty the bin (despite a promise to my wife that they would have another attempt on their return past my house) the bin remains full and I will have to empty it into bin bags and cart it over to the tip.