That is incorrect if a person is not appearing at a Port of Entry in which case they can be sent back to the USA under the Safe Third Country Agreement which only applies at the border.

Once they cross the border and are physically within  Canada then their refugee claim must be heard assuming that they are not ineligible per IRPA.  Making a prior claim for refugee status in the US or any other country does not render the claimant ineligible although it may be an issue that impacts the claimant's credibility.

There is no provision in the Convention that obliges refugee claimants to seek asylum in the first country they reach. Menjivar, Carlos Othmar Navarrete v. M.C.I. (F.C., no. IMM-9660-04)

Case law states that a negative inference can be drawn from a claimant's failure to claim in a safe third country, but it also clearly states that this failure cannot be a determinative.

Also a belief that a third country offers little chance of a successful claim is a valid reason.