Even though she was in office from December 2006 through July 2009, Palin’s governorship covers fiscal years 2008 (July 1, 2007 - June 30, 2008) through 2010 (July 1, 2009 - June 30, 2010), because those are the years covered by the budgets over which she presided.
I can see how that works out to three years of budgets; I guess it’s just that “2007-2010” sounds like 4 calendar years; in fiscal years, it should say “2007-2009”.
Virginia is interesting because we have 2-year budgets, so our off-year legislative sessions are “short” sessions, and just tweak the budgets rather than writing new ones.