Is this coin really worth $4,500?

The coin shown is a proof so it is one of the 26 that were minted. I would say today it would sell in the $10,000 range at least but I bet closer to $15,000. That is if it became available. A lot of rare coins once sold at auction do not go on the block again for a good number of years, or ever, if it went to a museum or a serious collector. Hope this helps