What is a reliable reference for "covering of the head during salah or otherwise is mubah" by men?

Most of the males in my place wear head covering with a cap or turban. Also some of the masjid have baskets full of caps for those who come to prayer without it. They don't say you have to wear them in order to pray, but you get hard looks at times. I have researched this and found that it is not a part of sunnah, but instead local customs or tradition. If we cover or not, it doesn't make any difference. Also the male head is not considered awrah. Also, men who are in ihraam pray bareheaded, because they are not allowed to cover their heads whilst in ihraam. This is solely my opinion from the research I have done. In my research, I found: what Imam Shafi'i had to say about this...its mentioned below:- > Imam Shafi'i said, "The covering of the head during salah or otherwise is mubah. Whoever claims that it is mandub, his opinion is invalid because of the lack of evidence in the chain of transmission; unless people use logic as evidence and this is not valid in our Shariah" (sunnah.org ) I'm seeking a reference for this. Also, I would like to know umar ra had said something in regarding this subject?