Edmunds isn't the only site with invoice numbers. If the Edmunds invoice number doesn't agree with KBB or Cars.com or MSN Autos, then maybe the number is wrong. Otherwise my guess is that the dealer has made up their own invoice. If so, you should let Costco know (I guess some Costco deals are either a markup above invoice or marked down from MSRP, so you may want to double-check that too).
From the Edmunds FAQ:
"Please note that the invoice price does not reflect any manufacturer-to-consumer rebates, the destination charge or the tax, title, license or registration fees.
Sometimes, however, the amount quoted as the "invoice price" includes the destination charge and sometimes it does not, so look closely."
Have fun shopping (and if you have the stamina for it, some dealers will beat a Costco price - the Free Price Quote service at Edmunds is relatively painless if you ignore the responses that implore you to come to the dealer for a quote).
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