I don't quite understand the logic behind this notion. Yes, there is a limit to everyone's strength and stamina, but every time you approach that limit, you're pushing it back a little farther.
Allow me to sort of draw an example of this, but using numbers. Say that your maximum "capacity" is a 10. Now let's say that during your day of training, you were able to reach a constant effort of about 8 or 9, sometimes maxing out at 10. After a day of rest and recovery, the next time you train, your maximum capacity might now be at a 10.5.
This is what training is. Maybe some people are naturally gifted with better stamina than others, but consistently training just outside of your limits is guaranteed to push them to a new level. Trying to exceed your limits all at once is where the danger lies.