From what I've been able to find, "facilitywide" is the proper term. However after a quick search I've been unable to find this term actually used. "Facility wide" and "facility-wide" are used about 50/50.
I looked up dictionary (http://www.dictionary.com/browse/wide) definition of "wide" and there it says: "a combining form of wide, forming from nouns adjectives with the general sense “extending or applying throughout a given space,” as specified by the noun: communitywide; countrywide; worldwide." Note the examples given at the end of the quote.
Best Answer
Hyphenation is the most inconsistently applied punctuation in the English language. Editors often have to look up whether a particular compound word is connected, hyphenated or open. This document, which runs to 10 pages, will give you an idea of the can of worms that you have opened. Your search having revealed that facility wide and facility-wide are used about 50-50 (hyphenation when expressing ratios is also correct, as the document will also tell you) only shows just how often native writers make mistakes in hyphenation.
In this case facility-wide is correct, both when preceding and following the noun it modifies. See the very last entry in the document: the rule for "wide" in a compound is that if you can't find it in the dictionary as a single word (such as worldwide) you hyphenate it.
Note that all three of the examples given in your dictionary example also have their own entries in the same dictionary. They are not intended to infer a construction that goes beyond the examples given.
The reason that some compounds are hyphenated and some are not has to do with how often they are used. As a hyphenated word gets used more often, the hyphen tends to drop out. For example, email was generally written e-mail back in the early 90s.