The OP was talking about inserting records into the ODBC table.
Presumably, running an append query based on a read only passthrough query won't work. Are you suggesting it will?
There is nothing to stop the OP from coding a pass through query with Mysql syntax that works on the server
"insert into tablename (colname) values (1)"
Or executing a stored procedure, to do almost anything (if such a thing exists in Mysql)
As mentioned previously, this suggestion was just a possible workaround for now, not meant to discourage the OP from discovering the cause of their original problem, if possible.