Yes, all that is true, but the inch measurement there is just a legacy from Chainmail, used in ad&d as a variable term of measurement. When it comes to what a square represents when using miniatures on an actual battle grid (ie. the equivalent of what we are discussing in this thread), page 10 makes it very clear that 3.33 ft. is the way to go.Page 60 of the DMG gives 1"=10' for combat. "The base speed is inches, indicating tens of feet in the dungeon or similar setting indoors, tens of yards outdoors."
Page 228 (Glossary) gives "Inches-One inch = 10 feet an the indoor (dungeon) scale; one inch =10 yards on the outdoor scale (See PHB, p. 39)."