Chola inscriptions call the vinayagar "Parivaara aalayathup pillaiyar" if I remember correct. Rajaraja leaves donations for daily supply of bananas & other things.
I happened to go through an 18th century palm leaf collection (called McEnzie collection or something). This is in chennai - aarasinar keezhdisai suvadigal noolagam (Tharamani). It has a long hear-say story about big temple. Neither rajaraja nor any of the known kings are mentioned - it says a king called karikaalan built it and goes at length to talk about many incidents during building of the temple.
Atleast few of the stories in there might have been real happenings. As time goes by imaginations get thickened - but some of the information might be real or close to reality.