LB: You are very close. The Mishna Berurah in 91:12 sates that “in our time, one should wear a hat on his head like he goes in the street, and not just with the ‘small hat’ that is under the hat because that is not the way people stand in front of important people” meaning that people did not go into important meetings without a hat on.
http://www.hebrewbooks.org/pdfpager.aspx?req=49623&st=&pgnum=244
The question is, can we now state that since in our time it is more of the norm to go with only a yarmulke can one daven without a hat? In my shul we have those who wear hats and those who only wear yarmulkes.