The Ordinary parts of the Mass (Kyrie, Gloria, Credo, Sanctus, Agnus Dei) if the setting is Gregorian and the Order of Mass parts pertaining to the people (responses), as well as any metrical hymn type procession or recession pieces can and should be sung by the people at a High or Solemn Mass. I suppose the people could sing a polyphonic setting of the Ordinary parts, but this is typically far too difficult. Furthermore I suppose they are technically allowed to sing the Propers but this usually too difficult as well.
A Dialogue Mass usually has no singing except perhaps a processional and recessional hymn. A Dialogue Mass is a Low Mass in which the people make the responses along with the server. The Ordinary parts of the Mass, the Order of Mass and the Propers of the Mass are not sung in a Low or Dialogue Mass. Dialogue Masses are not common in the USA.
So likely you attended a High or Solemn Mass, in which case the people’s singing was fully appropriate.