The "on" or "upon" preposition phrase in "Mary relies (up)on John" tells where Mary places, or rests, her reliance. "Rely on" is no more a unit than "sit on", despite the meaning being less literal than "Mary lies (up)on John."

There is nothing wrong with saying "On John she relied, to help with record keeping."

The "on" or "upon" prepositional phrase in "Mary relies (up)on John" tells where Mary places, or rests, her reliance. "Rely on" is no more a unit than "sit on", despite the meaning being less literal than "Mary lies (up)on John."

There is nothing wrong with saying "On John she relied, to help with record keeping."