It's funny, when I try to look it up, every other web page says something different.
The intensity of the light involved may play a factor as well. When we are starting seeds under fluorescent lights, they are getting a tiny fraction of the light that would be hitting them in the summer sun.
Here is a research paper from 2005 which found that using fewer lights on a 24-hour cycle was more efficient than using more lights on an 18-hour cycle:
http://hortsci.ashspublications.org/...2/374.full.pdf
That is obviously not the same thing as proof that tomatoes never need a dark period, just an example that seedlings can grow well in 24-hour light.
If I had to guess, if there was a need for a plant to have a dark period, then that need would probably be closely related to the intensity of the light involved.