"I consult with another mechanic who informs me that my vehicle has a canister type oil filter which has a check valve on it, and that if the filter is installed backward no oil will flow throughout the engine."
Personally, I wouldn't let anyone from Walmart near my vehicle, so don't take this as a defense of them.
One critical piece of info would easily prove this one way or the other. You didn't say that the mechanic actually did find the oil filter mounted backwards. That would have been the end of the issue.
The reason I ask is that it's unlikely you could have driven the car for most of the day without oil flowing through the engine. Your oil pressure light would have been illuminated as well. It's also unlikely that you would have been successful in driving the car for the rest of the week.
I can certainly see why Walmart would be skeptical of this claim. Additionally, by waiting a long time to make a claim, you make it look even more suspicious. Look at it from their point of view. You show up weeks or months after an oil change claiming that they damaged your engine, with a story that doesn't quite jibe.