I have had this happen unfortunately where the customer did receive free shipping and selected Priority Express which would have cost me $45 -despite the shipping time being the same as the lower level priority mail (both showed estimated 2 day delivery). I contacted the buyer and asked if they needed the production expedited/ needed to have their order before a certain date and they said nope! So I shipped their package with the regular priority shipping, they got the order as quickly as they needed it and I saved the ~$38.

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I think the only issue about not upgrading the shipping is if it will not get to the customer as quickly as they expect it or they paid for the expedited shipping and you're not honoring that.