VegasGambler

Well yes an instrument upgrade would be different, but that's not buying a first class ticket. OP said that they didn't know what the economy fare was, but no mention of an upgrade was made.

A y-up fare, or any fare that books into first class but has an underlying economy fare basis, is a first class ticket. They are entitled to the difference between what they paid and the cheapest (regardless of fare class) economy ticket.

Personally if I bought a more expensive fare class specifically to apply an upgrade instrument and was accommodated in economy, I would argue long and hard to be refunded the date difference to the cheapest economy fare class (including filIng a DOT complaint citing unfair and deceptive business practices if necessary, since the website claims I will be accommodated in first on that fare) but that's far less cut and dry and, unless the OP has left out crucial details, is not relevant here.

The fact that most first class fares have underlying economy fare bases is irrelevant and distracts from the relevant points.

Now, it's possible that $160 was the fare difference between what was paid and the cheapest economy fare, but that doesn't sound likely to me and as someone who (IIRC?) books a lot of first class tickets I'm guessing that it doesn't sound likely to you either? But yes, it's possible.