This is indeed unexpected behavior.
str="Conference room 1, \"John,
Please bring the M. Mathers file for review
-J.L.
\",10/18/2002";
ImportString[str,"CSV"]
Grid[%,Frame->All]
Indeed does not work as it should, what works slightly better is:
ImportString[str, "CSV", "TextDelimiters" -> "\"", "LineSeparators" -> {"\r\n", "\n", "\r"}]
Though it leaves some quotes. I'm not sure if we can tame the Import in 11.1.1 to make it work.
A little bird told me, though, that in the next version of Mathematica the CSV import will be redesigned, and the import works perfectly for your example without any optionsÂ…