Why is wearing a sheitel not marit ayin?

Question

I would assume that the concept of marit ayin applies to married women's hair covering (outside the home) as much as to any other mitzvah. So why do our poskim allow* her to wear a sheitel--which, in many cases, looks exactly like uncovered hair?

(There is a related concept to marit ayin called something like cheshed--wish I remembered the name--and I am wondering if it is that, too.)

It is somewhat widely acknowledged that the permissibility of sheitels constitutes a lenient (though mainstream) halachic ruling. So could it be that the Ashkenazic rabbis ruled thus because of the principle not to make a ruling that the people will not follow?

Related:

Can a Sheitel be made out of one's own hair?

Aren't wigs counterproductive?

--

*I am referring specifically to the lines "the majority of our Rabbis {rabboteinu} and also of those upon whom we rely fundamentally for ruling, permit."

Answer 1

Per this analysis:

R. Moshe Feinstein responds to the maris ayin argument in multiple ways: 1. A woman covering her hair is an obligation, not a prohibition (it is an issur aseh) 2. Someone, even if not everyone, can almost always tell when a woman is wearing a wig 3. People in our community know that women often cover their hair with wigs

His complete discussion of wigs in light of marit ayin may be found here.

Other halachic sources which argue that natural-looking wigs are unobjectionable are Shiltei Giborim on Rif, Shabbat 375, and Yaskil Avdi, Even HaEzer 16. (Credit for these citations: http://www.chabad.org/theJewishWoman/article_cdo/aid/840202/jewish/The-Lubavitcher-Rebbe-on-Hair-Covering.htm)

Another is P'ri Megadim, Orach Hayiim 75, Eshel Avraham 5, which draws from the Rema on the Shulchan Arukh, ad loc 75:2, and Darkei Moshe 303:6, concluding that "In those countries where women go out in uncovered wigs, they may rely upon the lenient view."

Another is Magen Avraham, paragraph 5, which characterizes as "questionable" Be'er Sheva's words (18) that "The permit to go out wearing a wig refers specifically to a wig covered by a hairnet."

Answer 2

As demonstrated in this answer, when a permissible alternative is common (in this case, a wig) many rabbis maintain that the issue of marit ayin is not a concern as people will naturally assume the woman is wearing a wig.

In this particular case, R. Shlomo Zalman Auerbach (Minchat Shlomo vol 2 58:29) applies the above rationale and thereby explains away the marit ayin issue; as does R. Yitzchak Abadi (Ohr Yitzchak vol. 1 EH §3), upholding the responsum of R. Moshe Feinstein mentioned in @SAH's answer.