The show was very much a real adaptation of Batman. Several episodes were based on specific issues. The show was a live version of the Silver Age Batman comic books. It may not seem correct to fans of Nolan or 21st century graphic novels, but it was exactly who the character was in print at the time.
This article in Forbes explains it in detail.
https://www.forbes.com/sites/scottmendelson/2014/11/11/the-batman-tv-series-is-the-most-important-batman-story-ever-told/#1cc53b483517