Not exactly correct nor wrong.  The solenoid is mounted to the starter, and
can be replaced separately.  Better question is why?  You had a weird a
occurrence that has happened one time.  Moving the truck had nothing to do
with it, just a coincidence.  Given the truck is now 7 years old, if your
going to change something, change the complete assembly.  But unless this
has happened often, I wouldn't worry about it.
I would follow Al's advice and pull the terminals off the battery and clean
them, you need to remove the bolts completely from the cable ends and then
carefully with a small flat tip screw driver pry the rubber grommet ends
back to expose all of the metal part of the terminal ends on the cables.
clean with a wire brush and baking soda.  Clean the battery connections as
well, If the bolts look nasty, replace them, less than a buck a piece from
most auto parts stores.    Use the same small flat tip to get the grommets
back over the metal part of the terminals.  If you look you will see an
"o-ring" like protrution on these grommets that fits in a groove around the
connection area on the battery.  Its designed to help keep the connection
clean, so don't cut the grommet off the cables.   Use a 5/16 6 point box end
wrench to tighten them and they wont strip.  Tighten the bolts snuggly, they
don't have to be king kong tight.

Whitelightning