I second what Newman is saying. Just like if you get mediocre grades in an SMP/Post-bacc, it often hurts you far more than if you had not completed them in the first place. This is sort of an analogous example to LOR that programs require. Sometimes grades themselves are not a good enough of a representation for admissions committees an they require letters of evaluation or recommendation from individuals who have "credibility" to pass judgement on the applicant. Usually with many letters of recommendation, the evaluator (physician, professor, etc.) is asked to rank this candidate against his/her peers to gain a context as to how strong this candidate is and a mediocre recommendation can be damaging in this regard.
Maybe you can go in and get to know a professor more that you have taken a couple of upper level division science courses with and recieved relatively good grades, B+ and up. Talk to him/her about your goals and if you recieve a relatively favorable impression that this professor is genuine in his interest to help you, then you can ask for a LOR while giving him/her a copy of your CV.
in my opinion (take it with a grain of salt), a great letter of recommendation from a physician/health professional is far stronger and more important than a great letter of recommendation from a professor. The science faculty LOR requirement imo is more of a reconfirmation that this student has academic competence, has a work ethic, etc. etc. but SMPs usually have an understanding that your academic background is somewhat troubled and are looking for reasons instead to ascertain how motivated you are of pursuing medicine which a physician can provide.
