I have both sticker and engraving Classics, so that part is likely legit. There seemed to be no rhyme or reason behind why they used a combination of the two types of case backing--I've seen Classic buckets from 1990 with engraving, 1991 with stickers, and 1992 with engraving (on Classic IIs).

That Classic on eBay doesn't seem to have a legit model number in its serial number.