I don't think so. See here (the green box in the upper right corner of page 2): https://www.epa.gov/sites/default/files/2015-09/documents/ep...
> nanograms per liter (ng/L) = parts per trillion (ppt)
Or alternatively: https://pubs.usgs.gov/circ/circ1133/conversion-factors.html
https://www.google.com/search?q=1+ng%2FL+in+parts+per+trilli...
If you check the second search result (https://www.llojibwe.org/drm/environmental/content/concentra...), it also corroborates what I'm saying:
> 1 nanogram/liter (ng/l) = 1 ppt
Technically speaking, ppt/ppb/ppm should be used for dimensionless quantities, but the convention used here is kinda contrary to that. The argument for the convention is something like this: 1 L ~= 1kg of water, so 10^-12kg of something per 1 L of water can be considered as dimensionless, since the kg and the L cancel out.
You could argue that it's still wrong though, in the sense that the website is in English, and currently the short scale is used in all main Anglosphere countries. [1]
P.S. I just realized that even the short/long scale thing doesn't explain the endmemo.com claim. It's probably just a mistake. In the short scale, a trillion is 10^12, while in the long scale it's 10^18. So, if we were to use the long scale, 1 ppt would a smaller unit by a a factor of 10^-6 (not 10^-3), and equal to 1 fg/L (femto is the SI prefix for 10^-15, while nano is for 10^-9).
In other words, 1 ng/L = 1,000,000 part per long scale trillion.
[1]: https://en.m.wikipedia.org/wiki/Long_and_short_scales#Short_...