CyranoJ
Ustuzou
- Joined
- Mar 5, 2015
- Posts
- 2,782
All of the online dictionaries that I just checked define "reserved" or "conservative" used in this context as "buttoned up" - most likely it does come from the notion of all the buttons being done tightly up.
From the Cambridge English Dictionary online:
buttoned-down said:formal and old-fashioned or boring:
a buttoned-down accountant/lawyer
How well will Landman's laid-back attitude merge with the more button-down style at Hughes Electronics Corp.?
Merriam-Webster agrees, so pace oggbashan I don't think it's a question of differences between American English and the Queen's.
However, you have a point, it does look like "buttoned up" will also serve. So everybody's right!