That used to be true, but no more. Belize Bank has about a dozen ATMs around the country, including one on Front Street in San Pedro, that will accept foreign ATM cards on the PLUS and CIRRUS networks. First Caribbean Bank (formerly Barclays) has a few ATMs that also accept foreign cards, but none in San Pedro.
Cash is dispensed in Belize dollars.
To be safe, it's a good idea to bring a mix: ATM card, cash, TCs, credit cards. The ATM might be down when you most need it.
And, as they say, bring half the clothes and twice the money you think you'll need.