It's a bit misleading: he's referring to the Cortex-M series of ARM microcontroller cores, which do not implement the core ARM instruction set but instead only implement the Thumb series of alternate instruction sets that are optimized for code density. There are older ARM cores that pre-date Thumb and only have the core ARM instruction set, but there would never be a situation where you'd want to take binaries compiled for one of those devices and run them on one of the microcontroller cores.

There are however, plenty of other variables across the ARM ecosystem that can cause real headaches, like the different versions of the VFP floating point co-processor.