It's funny that you mentioned 'proper', because that's not a true musical term. That's why you won't find anything on it. You may find someone's interpretation of loose phrasing, but they are not breaking the words down to its simplest element to make sense of it.
Let's look at the word phrasing. In a musical setting, phrasing is defined as a "short musical thought typically two to four measures long closing with a cadence (source: m-w.com)"
Melodies are often described as being made up of phrases. A musical phrase is actually a lot like a grammatical phrase. A phrase in a sentence (for example, "into the deep, dark forest" or "under that heavy book") is a group of words that make sense together and express a definite idea, but the phrase is not a complete sentence by itself. A melodic phrase is a group of notes that make sense together and express a definite melodic "idea", but it takes more than one phrase to make a complete melody.
So, if it's a loose phrase, the next logical step would be to negate the term phrase or phrasing (in musical terms) - one would have to place a group of notes that does not make sense together to express a definite melodic idea.
In the example on gospelchops.com, the terminology does not match the demonstrated style of play, hence making loose phrasing a slang term (I won't use Ebonics, because I hate that term; every race uses sland, but they don't say '
Wonics', but I digress). There was another person prior to your inquiry on another forum with the majority of the members being my brothers from a another mother (cited example:
http://www.pearldrummersforum.com/showthread.php?t=130331&highlight=gospelchops), and hardly anyone had a concise definition of the term. I think that username Coach McGuirk said it best in terms of what he feels that loose phrasing means.