I'm not a cardiologist. Maybe max hr doesn't change and it's all a matter of perception but I can say that the max hr that I could reach when pushing myself as hard as I could certainly changed. There may be some theoretical number that doesn't change but when your lungs aren't delivering enough O2 and your muscles aren't using what they get efficiently and your heart isn't strong and you're overweight by 50lb you'll find yourself huffing and puffing and getting aerobic at a pretty low heart rate. In my case I absolutely was pushing as hard as I possibly could and would be anaerobic and totally shot when my heart rate got a few beats over 130 and an all out effort could get me to 138 before I would be completely blown out. Fast forward two years, drop that 50lb (actually I've lost 95lb total), add 10,000 mi of training and I was able to sit for 20-30min at a heart rate of 153 and I could maintain 140-145 for reasonably long periods. I recorded max HR around 174 in all-out efforts.
Previously it would have been absolutely impossible for me to get my heart rate up to 155 let alone 174. That change wasn't a matter of not being able to stress my body and simply learning to push harder. I would be totally anaerobic at a much lower heart rate, unable to push and further and that is pretty much the definition of max HR.
Your max hr isn't just a matter of the heart...how hard you can push depends on your lungs, muscles, arteries and all sorts of body/fitness issues are affected.
Personal stories don't count for much; perhaps there -could- have been some way for me to ride harder and get my HR up further but I don't think so. Possibly the term max hr is being used differently here, but I can say that with a sweat inducing, gasping for breath full tilt effort I used to only be able to get my HR up to 135 and a few years later it was 175.