This is a classic dispute when it comes to the 68000. I'm inclined to agree with your perspective, actually, but my impression is that it's highly contested.

Commodore and Atari marketed their 68K machines as 16/32-bit, which is I guess technically the most correct. And other 68000-based machines, like the Sega Mega Drive/Genesis, were marketed as 16-bit - it even says it right on top of the unit!