I can't offer an authoritive source. However there is another expression, 'I can't trust him out of my sight' that makes the meaning obvious.
Most children go through a stage where their parents must keep a careful eye on them to prevent the child getting up to mischief. The parent might say, "Now he is a toddler, I can't trust him of out of my sight. He is always poking his fingers into everything and I'm worried he may electrocute himself or pull the bookshelves on top of him." This literally means that the parent is happy only when they can see the child.
When you can trust someone as far as you can throw them, it is just an exaggerated form of the previous expression. It means we can trust them at zero distance, i.e. not at all. We usually say this about adults and of course most people cannot throw another adult any distance at all.
EDIT
I've found some more evidence as to how the phrase may have developed.
If you haven't got any confidence in a man, you can't say much worse
of him than this — ' I'll trust him as far as I can see.'
The City Road Magazine 1874
Ye cain't trust him as far as ye kin throw a b'ar. That's why we call
him Snake.
Boys' Life - Aug 1930 - Page 22
I know all about Otto Ernsthausen. I wouldn't trust him as far as I
can spit!
Big Show By Charles Cooke - Harper & brothers, 1938 - 358 pages
P.S.
However A Dictionary of Catch Phrases By Eric Partridge traces it back to 1870.
P.P.S. I think I've beaten Eric Partridge with this !
Somethin furthur,' siz I, ' than I'd trust you.' 'How far is that?' siz he. “Just as far, then, siz I, as I could throw a bull by the tail. The Westminster Review - Volume 9 - Page 434 - 1828
Best Answer
It doesn't appear to be a commonly known Swedish word, but rather a term coined for a specific purpose: Swedish coach Gösta Holmér developed the fartlek training method in 1937.
The method was introduced to the US in the 1940s, after two Swedes made it famous:
The earliest citation in the OED is from a 1952 Scholastic Coach:
An earlier snippet dated 1950 from the American Athletic Journal (by the National Association of Basketball Coaches of the United States and American Football Coaches Association) has a note from the editor saying this training method is spreading globally:
And a book called Fartlek: The Swedish Distance Training Technique, from Track & Field News, March-Sept., 1949 was published in Los Altos, California. Contents:
The technique was further described in American and British running and physical education publication in the fifties.