Grievances are always grievances, if they are genuine irrespective of the sources from which they are collected. How to bring them to the notice of the higher authorities for taking appropriate remedial measures depends upon your communication skills so that unnecessary escalations can be avoided.
What ever discussion took place during one to one meeting can be documented and can be forwarded to Management. The purpose of one to one session is that Management want to know the views of employees about the day to day employment practices and to make corrective measure if required or to explain the situation to employees.
However exact translation to Management " as it is " shared by employee may aggravate the Management. For example instead of presenting " Mr._____ was very much angry about company's policy decision" this way the same can be presented in polished words
"Mr.____ expressed his concern over the company's policy decision". So communication matters.