Thanks for your help.
Good news: Line based importer brings in all my rows.
Bad news: The CSV file escapes commas that are internal within the field using quotation marks. The command in Open Refine, Edit Column-->Split into several columns does not pay attention to the comma escaping with quotation marks when splitting by comma. There is probably a regular expression way to split this and I'm just not adequately caffeinated to figure it out.
My workaround for the time being, is to open original CSV file in MS Excel (the file did not originate in Excel), save as tab-delimited text, then import to OpenRefine. I would be open to more elegant solutions.