I think that statement is misleading. You don't "damage" your joints by doing maximum lifts. Yes, there is more stress per repetition, but you are doing far fewer repetitions. I'd like to see some evidence supporting this, because virtually every certification organization out there teaches you how to test a client's 1RM, and suggests doing so as part of an assessment. Hell, I would be more likely to argue that running at a high volume is pretty stupid and likely to lead to injuries, but most people deem that to be a healthy and safe activity.
You can exceed the tolerance threshold of a tissue via cumulative trauma, or an extremely high level of acute trauma. Typically, you aren't going to come anywhere near exceeding the tolerance of a tissue to stress when doing a 1RM attempt if you are a natural lifter. Generally, it is cumulative low level trauma that lowers this threshold over time, making it appear as if the heavy weight is what "caused" your injury.
This is why it is commonplace for someone to throw out their back picking up the phone or a pencil off the floor. It's not that the pencil was too much for them, it's that they repetitively stress their tissue (In this case probably sitting all day long) to the point where a given tissue is deteriorating, and the pencil is the "straw" that broke the lifter's back.
Honestly, I think the biggest danger associated with 1RM testing is form breakdown. It's obviously more difficult to maintain proper form when at the limits of your force production capabilities. However, this is not always the case. I have seen some pretty textbook maxes from powerlifters when they are pushing themselves to exceed their competition 1RMs. As well, this danger is just as great with higher repetition lifts. I think we have all, at one time or another, eeked out that 10th repetition when it wasn't too pretty.
People say this all the time about maxing out on lifts, but what about sports? In most sports you push your body to the limits, and you subject your joints and tissues to much greater stresses than you will ever see doing a 1RM. Just look at the injury rates for various sports. Weightlifting, where the competition is basically reaching and exceeding 1RMs, is very low injury compared to basketball, soccer, endurance sports, or even golf.
With that said, I agree on some level. 1RM testing is just not necessary for most people, and I rarely do it with my clients unless they request it. I would obviously do it for a competing powerlifter too, but that is far from the demographic I work with. You can get a fairly accurate estimate by testing a 3-5RM if you are looking to gauge strength.
