Of course, seconds after asking the question I found the answer.
The SelectCommand I'm using to actually fill the DataTable looks like this
da.SelectCommand = new SqlCommand("SELECT Id, FirstName AS Fornavn, LastName AS Efternavn, " +
"TcReadOnly AS 'Read only' FROM PersonTable", sqlConn);
Which means that the columns in my DataTable doesn't have the same names as the ones I'm trying to update the database with :-) Brainfart....