Okay ... I've had a couple of years to ponder this one and I'm officially declaring the 'Roman burnt toast' thing not classical. I first came across it a couple of years ago (here's another notice of same) and as might be expected, it comes around again at this time of year. Our exemplum this year (from the Examiner) is rather more detailed:

Floating a burnt piece of toast on top of wine was actually a way to take away some of its bitterness and acidity in ancient Greek and Roman times. The wine was far from as good as what we enjoy today and the charcoal tempered the wine's acidity. The word toast actually come from the Latin word tostum, meaning to burn or scorch.

The more usual exemplum is the sort of thing we get from the Marco Eagle:

The term “toast” came from Italy where the ancient Romans placed a slice of toasted bread in wine to signify and celebrate good luck.

Here's the skinny: "Tostum" does actually exist as one of the principal parts from torrere, but in Classical Latin ALWAYS seems to mean to burn or scorch. None of the listings in Lewis and Short mean otherwise and, interestingly enough, I don't see any which refer to 'toasted bread' (if such does exist, please correct me).

Turning to the various listings in various dictionaries under "toast" at Dictionary.com, the participle form is cited several times as the vulgar Latin origin of the word. However, when we look at the the Online Etymological Dictionary entries, we have two very interesting entries for the noun "toast" referring to bread not being used before ca 1430. The use of it in the 'New Year's' sense dates from the end of the 17th/beginning of the early 18th century.

I think we need to begin to keep our eyes open for the assumption -- which I think this is based on -- that if something has a Latin word it must needs have a Roman or Greek origin -- I suspect the Greek connection comes from the assumption that everything the Romans had must have come from Greece (and by further extension, everything the Greeks had must have come from Egypt).

A history of the toast (Examiner)
Celebrate the Season (Eagle)
toast (Dictionary.com)