The web page you reference is old (note the cvstrac portion of the URL, which is the giveaway; sqlite uses fossil now, not cvs). The newer version of that web page is here.
Since SQLite is public domain software, one solution to your problem is to fix sqlite's shell.c to handle your file format correctly. The problem is around line 1861 that does
if( c=='"' ) inQuote = !inQuote;
If you don't want quote delimiting, just comment out this line. The purpose of the line is so you can embed delimiters in your columns by quoting the column.
Another approach is to use a Database Manager that supports SQLite; there are many of them, and most claim to support file import/export.