Hi Masa,
Your understanding is correct but let me clarify further as it's purely a semantic issue potentially. "task type" within group by is different to "task type" within filter and multiple selection. In the world of Fiori, the one label shouldn't be used for 2 different pieces of data.
Note - A single inbox is usually what people want in Australia (maybe from a CIO perspective only???) so might be a country preference (e.g. This is the requirement at multiple companies I've come across) - and why My Inbox is such a good architecture.
Cheers,
Matt
ps. If people could save their group by preferences, I think it would probably get better adoption.