Is it possible? Yes. Is there conclusive evidence? No.

Construction began in 1848, and the marble used came from Cockeysville, MD. The quarries in this area were heavily used throughout the capital, to include the U.S. Capitol Building, (which is positively identified as having been built with the use of slave labor) and there are records of slaves being used to mine marble in and around Cockeysville. That being said, there are no definitive records that show slave labor having been used to mine the marble used in the monument, nor in the construction.

Though not structural, there were a number of commemoration stones donated by states, major cities, private organizations, and foreign powers. These stones came from locally sourced marble, and slave labor would have been commonly used in those quarries which were in slave-holding states.

We can also safely infer, given that donations were accepted from across the country towards construction, that at least some portion of the funds used came from the profits earned from the fruits of slave labor - both directly from slave owners, as well as indirectly from northerners who used the fruits of slave labor in industry (such as cotton textile mills).

So ultimately it depends on how narrowly you want to define the term "built by slaves". Slave labor may or may not have been involved in the quarrying and installation of the structural portion of the monument. We can, however, accurately infer that slave labor would have been used in mining at least some of the commemoration stones and in the funds used to pay for supplies and construction.

Maybe the author is implying that the 'free citizens' are somewhat slaves...