Is the philosophy then that, when plants have everything they need, they successfully out-compete algae?
I always hated the "out-compete" claim. It's inaccurate. If there's competition, then something must be limited. But in EI, nothing is limited.
So we can't claim competition, unless it's for something else that we're not adding - which the algae needs, and the plants do not yet will still use and eliminate. Possible, but not proven, and certainly not the only possibility.
To tell the truth no one really knows why it's possible to grow plants without algae. There is little scientific or empirical evidence that directly applies, and likely not to be any for a long time, as there's just no environmental or economical reason to perform such research.
However, that's a very limited view. Instead view every planted tank hobbyist as a researcher, and every tank as an experiment. Now you have thousands of long-term studies in progress, and though individually they aren't as controlled or in agreement as some would like, together their scope greatly exceeds that of any traditional scientific study.
But it is of course up to you to interpret the results.
To sum up my interpretation:
1) Provide all the plants can actually use, and little more. If there's any question, always err on the side of excess, which is tolerated far better than deficiency.
2) Algae is initially caused by poor plant health or conditions, but once present, it seems to create conditions favorable for itself. Use its presence as a sign that you may not have fulfilled #1, but if you're certain you have and the algae still persists, attack the algae directly.