Therefore MtGox's prices are higher due to a BTC shortage, not a ca$h shortage.
Correct, the inability to get ca$h out of the exchange in a timely and reliable manner creates a surplus of ca$h already in the exchange. The fastest way to withdraw value from the exchange is to convert the ca$h into
BTCTC, withdraw the
BTCTC, and sell them elsewhere. This outflow of
BTCTC creates a
BTCTC shortage. The ca$h surplus and
BTCTC shortage naturally results in an increase in exchange rate as expressed in the form of $/
BTC (or a decrease in exchange rate as expressed in the form of
BTC/$).
That's a problem local to Mt. Gox. Legit exchanges where you can get money out don't have that problem.