It is easy to be myopic about silent films in sites like this and elsewhere, but believe it or not, music and theater was around a long time before silent films and Hearts and Flowers is one such example of "silent film" music pre-dating the films themselves.
Prior to my work in silent films I worked for many years (and continue to work, BTW) in theater and dance. H & F is also a popular theme in melodramas which would account for the time period you see in the always questionable Wikipedia.
As a musician circa 1970 I was using this tune from time to time (usually more in a comedic context than a serious one). That was a full 16 years before I first accompanied a silent film. So yes, it is "really true" that H & F predates silent films.
In fact, you can hear a sample here:
http://www.folkways.si.edu/trackdetail. ... emid=24659
This a recording where the tune is used in a music box in the 19th century, perhaps for a carousel.
BTW, the composer was: Tobani, Theo. M. (Theodore Moses), 1855-1933
The copyright on the simplified piano version is 1909.