For practical purposes, she’s wrong. You melt down scrap sterling
silver, and you end up with metal that remains sterling silver.
You’re correct as well, that if you’re melting scrap that contains
solder or other non-sterling componants, then the result will also
not be quite sterling.
To be really picky, though, when you melt sterling silver in any but
the most controlled situations, some small percentage of the copper
will get oxidized. The result is that over many remeltings, the
percentage of copper slowly gets reduced, raising the silver content
slightly above the definition of sterling. You can still stamp this
metal sterling, as it’s better than sterling. And this effect is
small, needing many remeltings of the metal before it becomes
measurable by any means normally available to the jeweler. But it is
this slight reduction of the copper content over time that means
that technically, your instructor is possibly right. But in practice?
However, one other aspect to consider is not whether it remains
sterling or not, but just the quality of the metal you end up with.
Remelting the sterling can introduce slight additional impurities,
mostly bits of copper oxide or the like, that can affect the final
quality of the sheet metal you’re making. If you’re melting
technique is good, this isn’t a big problem, but over time, scrap
metal can be harder to get consistent good sheet metal from…