Who Laid the Cornerstone of the Washington Monument?

In many references, I see that the stone was laid on 7/4 of 1848 in a ceremony attended by president James K. Polk. However, in all references to the mysterious death of president Zachary Taylor, he is said to have contracted either cholera or heat stoke while attending the same ceremony...but exactly 2 years later, on Independence Day of 1850. Can anyone clear up this paradox?