Unless there are more recent statistics on SNAP usage than the official statistics available from the US Department of Agriculture or someone has a very creative definition of "highest useage", the statement is false. If we go back a few years, the statistics may however back the claim.
In the statistics, there are two different values, which both could be described as "usage" in a colloquial language. One value is the ratio of the population receiving SNAP benefits, the other value being the average benefit amount per inhabitant.
If we take a look at the latest statistics from 2010, 52.08% of the population in Owsley County received SNAP benefits, ranking Owsley behind Shannon County, SD (59.33%), Todd County, SD (55.08%) and Wade Hampton, AK (54.13%). If we go back to 2008 and earlier, Owsley County was indeed in the "lead", but the three other counties passed Owsley in 2009 when it comes to number of recipients per population count.
If we look at the average payment per inhabitant, Owsley is even further down the list. The statistic contains however some very strange numbers, which seem erroneous to me. E.g. Hopewell City, VA with a population count of 22655 allegedly received $243,376,900 in SNAP benefits in 2010, making an average monthly payment per inhabitant of $895.23, or per participant of $3,051.67.