Not true at all!
My club, Bromley RFC, has a veterans team many of whom are over 40, they are still trying to get me to run out and I am 48, and 4 regular teams. And, I know of several other clubs in the area which have similar setups.
Look in your local area find one or two clubs and pop along and have a chat I am sure you will find something for your level even if to start its a bit of training and some tackling drills.
For the most part rugby at club\amateur level is very much about the taking part as much as results