I have to be careful not to offend people when I try to answer these questions.
As the excerpt implies, the problem with "sentence a" is that it is not a complete thought. It is missing part of what is necessary to compare by use of the word "than". Now 'sentence a' will sound fine to most Americans, but that is because most Americas are content to write just as they speak. That is another issue. Moreover, just because a sentence is 'grammatical' does not mean it will make sense. The sentence: "The tree ran flatly" is grammatical but makes no sense.
In the example you cited, let us say you changed the nouns:
E1: We invited more people than wanted to come.
E2: We invited more children than wanted to come.
The second sentence (E2) is structurally just like E1. However, think of what could possibly be added as a comparison to "more children than". For example E2 could be:
E2a: We invited more children than children who wanted to come.
E2b: We invited more children than adults who wanted to come.
E2c: We invited more children than neighbors who wanted to come.
E2d: We invited more children than chaperones who wanted to come.
As the excerpt explains, it is because the original sentence is missing "… the necessary parallel structures…"(i.e. the other part of what is being compared) that causes the word 'than' to lose its power of comparison.
The original sentence is grammatical, but is incomplete as a thought. That is why it sounds "odd" to me and why I would not write it as originally composed.