While I cannot speak to the veracity of the video, gutter oil is mentioned enough times in other verifiable sources to make it a reasonably accurate story. An article in Bioresource Technology mentions "popular concern on food security caused by illegal use of gutter oil in China" as well as "producing biodiesel from gutter oil."1
There is another article in the Journal of China Executive Leadership Academy with the title "Dilemma in the Supervision of 'Gutter Oil.'"2 It starts like this:
For quite a long time,alluring profits and absence of effective supervision jointly contribute to the rampancy of "gutter oil" business. Besides,there lack of relevant laws and regulations to curb the production and sale of "gutter oil."
Another paper, in the Journal of Instrumental Analysis proposes to use gas chromatography-mass spectrometry to distinguish gutter from edible oils.3
Finally, there is a the wikipedia page on gutter oil, with even more sources.
- Sai Liang, et al. "Life cycle assessment of biodiesel production in China." Bioresource Technology, Volume 129, February 2013, Pages 72–77.
- Wang, Dang. "Dilemma in the Supervision of 'Gutter Oil." Journal of China Executive Leadership Academy, 2012:05.
- Hui-qin Wu, et al. "A Novel Method for the Identification of Gutter Oils Using SPME/GC-MS." Journal of Instrumental Analysis, 2012:01.