And how could you miss a rat in a canoe for 1000 miles? In a european medieval ship I can see it happening but there's no evidence that these people built anything more than tree trunk canoes.
They may well have been intentionally introduced. Here in New Zealand the Maori ate polynesian rats, and have a legend about how they were brought here [1]. Who knows whether the legend is based on an intentional introduction or not, but it seems likely.