A "Turn of the Century" Problem

Here's a problem for William Safire or Richard Lederer or some other language-usage maven to solve--the proper use of the term "turn of the century." It either means the end of a century or the beginning of one. The writers quoted below clearly don't agree on its meaning:

"At the turn of the last century[that is, at its end], the dot-com collapse made e-commerce a dirty word among investors as headlines proclaimed the death of online business...."--Alvin and Heidi Toffler, Revolutionary Wealth (Knopf, 2006).

"At the turn of the twentieth century [that is, at its beginning], Long Beach [on Long Island in New York State] boasted the largest hotel in the world, a 1,100-foot long behemoth that promptly burned down."--Edward Kosner, It's News to Me (Thunder's Mouth Press, 2006).

"When [Hubert Harrison, the Afro-Caribbean orator and thinker] moved to New York City at the turn of the twentieth century, [he] brought a multicultural Crucian* background, reading and writing skills, intellectual curiosity, and a feeling of oneness with the downtrodden--all of which would be important in his future work."-- Jeffrey B. Perry, Hubert Harrison: The Voice of Harlem Radicalism, 1883-1918 (Columbia University Press, 2009)

Which usage is correct?

*Harrison was born on the Caribbean island of St. Croix, in the Virgin Islands.