You certainly CAN scrub tile and grout with a rotary. Sometimes these boards cause new people to do some unnecessary things ... and it's a damn shame.
Get you two good brushes. I forget the gauges, but if you contact any decent supplier they can tell you what the are. Ones for really light scrubbing of carpets and it works on tile too, and the other is for commercial carpets and it works on tile as well.
Mikey is of the BB order that thrives on making things unneccesarily complicated.
You'll need a stand up grout brush for the edges. I haven't bought one yet, so I'm on my knees using a hand held one, and I can tell you that's a pita.