If the only financial institution in town is located on the only riverbed in town, is the sentence "Judy went to the bank" still ambiguous?

Nice try. But the answer is yes, it is still ambiguous. The river's bank is presumably much bigger than the financial bank, so "Judy went to the bank" could mean she is fishing on the river's bank outside the financial bank or she could be cashing a check inside the bank on the bank.

Now, if you had said that the only river in town is located entirely within the financial institution and the only place to be in the bank is on the bank ...

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