No, MySQL at its beginnings was just MyISAM. InnoDB was quite much later added to it, which was fine at the beginning. MySQL AB by the way, the company behind this database engine, was a Swedish.
InnoDB was though not a development by MySQL AB, but of Finnish software company called Innobase Oy Inc. InnoDB though was in 2005 bought by Oracle, meaning that Oracle controlled an important part of MySQL through this and many feared the worst that Oracle would try to eliminate through this graps its competitor. 2008 MySQL AB was acquired by Sun Microsystems, which later were 2010 bought by Oracle.
Since Sun/Oracle was giving MySQL quite long enough not much love, MariaDB was created 2009 by Monty Wirzenius, MySQL's original programmer, as dropin replacement for it with advanced features which MySQL not has.