Sentence Correction

I came across this old standard question and I ahve just 1 doubt about the modifier usage in the correct option.

Unlike computer skills or other technical skills, there is a disinclination on the part of many people to recognize the degree to which their analytical skills are weak.
(A) Unlike computer skills or other technical skills, there is a disinclination on the part of many people to recognize the degree to which their analytical skills are weak.
(B) Unlike computer skills or other technical skills, which they admit they lack, many people are disinclined to recognize that their analytical skills are weak.
(C) Unlike computer skills or other technical skills, analytical skills bring out a disinclination in many people to recognize that they are weak to a degree.
(D) Many people, willing to admit that they lack computer skills or other technical skills, are disinclined to recognize that their analytical skills are weak.
(E) Many people have a disinclination to recognize the weakness of their analytical skills while willing to admit their lack of computer skills or other technical skills.

In the correct answer D what type of modifier is the one that starts with a present participle 'willing'?. It looks like a 'present particicple' modifer separated by commas and hence should be a verb modifier. But in fact it is modifies people. Don't we need a 'while willing' or a 'who are willing'?

thanks,