It turns out that the opening of the hospital is often mis-dated as that 13th of April. Here are a couple references provided by a user validating the 18th:
<http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2610750/?page=1> and <http://www.nyc.gov/html/hhc/harlem/html/about/history.shtml>