Actually the law says that people can't be discriminated against in education or work if they can perform the "essential duties" or meet the "essential eligibility" of that job or educational program with or without reasonable accommodation. What constitutes a resonable accommodation isn't always clear cut, but if a person can't meet the essential requirements with or without reasonable accommodation then they can be legally turned down.
Here's something from the AAMC website since they can explain it better than I can.
http://www.aamc.org/newsroom/reporter/june04/word.htm
"Both public and private entities are required to provide accommodations to persons with disabilities so that they may enjoy the same benefits, services and opportunities as those without disabilities. In particular, during their admission processes, medical schools and other institutions of higher education are required to judge students on the basis of their capacity to complete the educational program, rather than on their status as disabled persons.
According to the ADA, students seeking admission to medical school must be able to perform the "essential functions" or meet the "essential eligibility requirements" of the program after being provided with the needed accommodations. Each school is responsible for determining the "essential functions" or "essential eligibility" requirements (i.e., "technical standards") of its educational program, and for establishing its admissions criteria with such definitions in mind. For example, a requested accommodation that would cause a school to fundamentally alter its curriculum is not a reasonable accommodation. Additionally, of course, when deciding whe- ther or not to admit a student with a disability, the reasonable accommodations required by the ADA cannot create an undue hardship for the institution. Schools obviously vary in their ability, financially and otherwise, to implement reasonable accommodations even if their technical requirements would permit the admission of a given student.
Determining the fundamental req-uirements of a medical school program entails more than a simple legal or curricular design exercise. When contem- plating such requirements, one is challenged to answer several questions, including: what does it means to be a doctor in today's society; what constitutes good doctoring; and what are the truly non-negotiable elements composing a basic medical education.
Take the hypothetical example of a straight "A" student with high MCAT scores who possesses all the intellectual and personal characteristics expected of doctors but who happens to be quadriplegic. The admissions officers review- ing such an application would need to determine whether their institution's essential eligibility requirements dictate that all students be able to perform certain activities that only the physically "unimpaired" are able to perform unaided, such as a complete physical examination and resuscitation procedures. In framing their requirements, institutions need to consider not only societal expectations of doctors but also how doctors are actually practicing in today's workplace."
Here's something else from a different website.
http://www.daisweb.com/node/53
"An accommodation is not reasonable if it poses a direct threat to the health or safety of others. In order to establish a direct threat, the institution must be able to document a substantial risk of significant harm. Concern about direct threat arises most frequently in relation to allied health and professional programs in which the students ability to provide safe and appropriate quality care is questioned. It should be noted that the mere existence of a disability does not provide evidence of direct threat. Nor does the possibility of a difficulty arising constitute a substantial risk of significant harm. While an institution may be able to make a case for direct threat in the instance of a deaf nurse or early childhood education major with limited vision, it would be a hard argument to make for these same students in an English or Philosophy class.
It is important to note that under the ADA the direct threat must be to someone else. The individual with a disability has a right to choose to assume the risk to self in the same way that anyone else who participates chooses to assume that risk. A blind individual could not be denied participation in a hiking class that covers rough terrain because of a fear that he/she might trip and fall, but it might be appropriate to deny participation to this individual in a scuba diving class in which participants are paired up and responsible for monitoring each others safety through the visual inspection of valves and gauges."