Not as true as you think.
Switching up can have its benefits. Obviously its BS if you do it often (ie every 3-4 weeks or so) but switching up and tweaking a program slightly after a period of say 3-4 months (or a couple of cycles) can be VERY beneficial. just off the top of my head:
1) Hitting different muscle heads - especially on isolations.
Can you keep doing those bicep preacher curls? Sure you can! Doesn't mean that switching it up with a cycle or two of Hammer Curls (to emphasize the long head of the muscle) won't give you a growth spurt. Especially if your training routine hasn't already been prioritizing working both bicep heads.
2) Hitting different muscle groups that may be lagging - both isos and compounds.
Going back to the hammer curl example, IF the trainee hasn't been doing hammer curls, he could very realistically be lagging on forearm development (a less glamour muscle that don't get much love sometimes).
Forearms are really important and the added grip stability can really allow you to bust barriers especially with regards to weighted pullups or even deadlifting.
For larger muscle groups especially (lower body and back) switching up is not only good but essential provided its done right. Squatting is wonderful but don't come here and seriously tell me you get great hamstrings or calves from squatting alone. Iso work like hamstring curls or calf raises is required. Given that there are a lot of individual muscles involved in the back or lower body, one can't always be sure he/she is giving them all an equal amount of development given a busy schedule. Even assuming devoting 1 iso exercise to a body part is no guarantee that certain muscles are not lagging due to undertraining or genetics. Blindly forging ahead month after month with the exact same set of exercises instead of a well-planned tweak to focus on the weaker group will only lead to imbalances which will sooner or later lead to injury.
And what about right/left imbalances or anterior/posterior imbalances. There are a heck of a lot of possibilities to simply write off "switching it up" = bad, which is as retarded as those who think switching up every 3 weeks is great.
3) Body kinesiology, everyone is different.
Are squats great? Hell yes!
Are squats equally great for everyone? No.
There are certain individuals that find better stimulus and growth with hack squats due to femur length.
Similar for deadlifts. There are way more variations that the standard deadlift, one of those may or may not be optimum for you but how would you know if you never bothered to find out?
We could go on for hours here.
I would say that IMHO only your body can tell you what works and what doesn't. Having a training log and religiously tracking body size is far FAR more important than having a variation = bad/good attitude.
And why the hate for flys? Marvellous exercise, even for beginners.