Yes they do integrate with Reckon Accounts Hosted. You might be typing the file path wrong.
File path is:
File is under Q Drive: Q:\File name.QBW
File is under Shared folder: \\SharedFolderName\File name.QBW (remove any numbers before and after the company name in the shared folder. Browse to your Q drive to find out the shared folder name or after opening a file, press Ctrl 1
Did you talk to Autoentry to see if they can assist you?