It's all PR BS I'm afraid. I was told by somebody on the project a few years back that it was a myth that the bridge was constantly being painted. Futhermore he said he could cite periods where no painting was done on the bridge at all for some considerable time.
The whole myth got started because painting the structure is so complex that it obviously takes a very log time and somebody stated that it took so long that by the time the painters reached the far side they would have to start again at the other. There was never any official confirmation of this.
Indeed I remember a few years ago it being a news story (probably in the Scotsman) that the bridge was falling to bits because the painting had been stopped. They can't have it both ways - either the painting was stopped or it has been continuous since the bridge was erected.