I found that reference and yes it is for an earlier engagement, but it probably came after the authorization from New York (April 17 vs. a presentation on July 4). The New York Adjutant General's Report groups their regiments with those from Mass. and Penn. for the activities in Baltimore:

"To these regiments, together with those sent forward at the same time from Massachusetts and Pennsylvania, belongs the honor of having been the first to march."

From the book "Historical sketch of the old Sixth Regiment of Massachusetts Volunteers" describing the events of July 4, 1861:

The next day it returned to the Relay House. The Declaration of National Independence was commemorated on the Fourth of July and a magnificent silk banner was presented by loyal citizens of Baltimore, bearing this inscription: "Loyal Citizens of Baltimore, to the Sixth Mass. U. S. V. Pratt Street, April 19, 1861."

Ed