不管对与错,出题人是这样考虑的：
Students (WHO ARE) worried about their finances can request a smaller room ---------原本是定语从句,出题人省略了who are,这样,worried about their finances这个分词结构 就成了students的定语.
如果是worrying- -- - ,也是对的：
worry about- - - -
be worried about -- - -
只能说,是思维的角度不一样吧.