My friend Rabbi Ari Kahn informs me that rapeseed is grown near wheat fields. Hence, he avers, no reasonable Passover supervision is feasible for rapeseed oil.
What does one do? One Googles.
What does one find? Overwhelmingly the Kashrut supervision sites say: Besser Nisht.
I'm still not convinced. Isn't possible Hametz (assuming that's true), battel before Pesah? The oil is denatured and re-processed. Doesn't that militate against both a kitniyyot designation and a ruling of חוזר וניעור? R. Moshe paskened that even in cases where it's difficult to sort out the species, the prohibition is restricted to legumes that were originally banned. וואו שטייט אין דברי הראשונים אש מאן טאר ניט עסען רייפ-סיד אוף פסח? [UPDATE: No Rishonim, but a מחלוקת אחרונים. See Resp. Avne Nezer, Orah Hayyim no. 373 and Resp. Maharsham I no. 183. The latter explains the odd formulation on the הכשר. See the next update.]
I welcome any and all responses.
I'm grateful for all of the responses. Despite the fact that the בעסער נישט opinion is quite common, there is a very strong case to be made for allowing Canola Oil. The major points are provided in a review by the Rav of Alon Shvut (2), R. Yosef Zvi Rimon. The article is not on the VBM website. I'll be happy to send it along to anyone who asks. (Thanks to Rabbi Professor Dov Frimer שליט"א for sending it along to me.)