Did they see you possess or throw away the knife? If no, then no, the DA has no case.
Definitely worth fighting if they press charges. Good Luck.
Mr. Feasel is a former Deputy DA in the SF Bay Area with over 10 years of criminal law experience. Nothing stated on this site shall in anyway be construed as legal advice, or as creating any attorney/client relationship. If you would like to hire Mr. Feasel to further investigate your situation, feel free to contact him thru this site.
Mr. Feasel has responded quite accurately. The big question is whether they actually saw you possess or throw the knife under car.
You should consider fighting this charge.
Not a very good case, but you need to be careful making statements like this on the internet. Though it would be very difficult for the DA to trace your post back to you, it is generally unwise to make admissions like this online.
But again, to answer your question, the case sounds terribly weak.