that's what I found at M-W:
Main Entry: 2outfit
** Inflected Form(s): out·fit·ted; out·fit·ting **
1 : to furnish with an outfit
2 : SUPPLY <outfitting every family with shoes -- Amer. Guide Series: Vt.>
intransitive senses : to acquire an outfit http://www.m-w.com/cgi-bin/dictionary?book=Di...
outfitted adj. : 1. Equipped with appropriate wearing apparel and accessories; "children properly outfitted for school."http://www.ultralingua.net/index.html?service...
as well as at AHD:
tr.v. out·fit·ted, out·fit·ting, out·fits
To provide with necessary equipment: This store outfits skiers. See Synonyms at furnish.
Source: The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2000 by Houghton Mifflin Company.
At least there's one indication in support of 'fitted out' at:
adj 1: furnished with essential equipment for a particular occupation or undertaking occupation; "well-outfitted expedition to the South Pole" [syn: fitted out] 2: equipped with appropriate wearing apparel and accessories; "children properly outfitted for school"; "equipt in the...national dress of the Scottish people"- Sir Walter Scott
Source: WordNet ® 2.0, © 2003 Princeton University http://dictionary.reference.com/search?q=outfitted
But, as a non-native, I'd easily could be proven wrong for stilistic (or whatever) reasons when relying on dictionary entries only.