Well, it might be about how the shrink and the neighbor's paths first crossed. Maybe they met at a local event and the shrink's professional identity came into play right away. Or perhaps the neighbor had heard about the shrink through the grapevine and approached him with a problem that was the start of this whole story. It could also be about the setting where they live, like if it was a small community where everyone knew everyone, which affected how their relationship developed from the very beginning.
Definitely not a true story. 'The Shrink Next Door' is made up for entertainment purposes. It doesn't draw from any real-life situations or individuals.
The back story probably has to do with the shrink's practice and how he came to be involved with the neighbor. Maybe he was new in the area and the neighbor was one of his first clients in the neighborhood.