Students/employees that have accommodations have them so they can perform or learn based on their abilities rather than their disabilities, but they are NOT excused from requirements that are deemed essential to the program/job.
KJP: If the school didn't think it was essential to have a hard time limit on the testing for the disabled student, then it must not have been considered an essential academic requirement. It might have been a good issue to bring up with the program if it seemed like the program was treating timeliness as essential to some students and not others.
I've included some info below on the use of accommodations in higher education and the workplace.
Regarding Employment:
The protections for the disabled depend on the ability to perform essential job functions (in the US). If producing written work quickly is an essential job function, a person who could not do that would not be qualified for the job. The disabled person (or any person) needs to look for a job that is within personal abilities. And no company or law firm is required to hire or retain someone who cannot perform the job.
Most job descriptions will list essential (and sometimes nonessential or marginal) functions of the position. An applicant typically has access to this information before applying for the job.
Here's a link regarding that, followed by a quote from the linked page:
http://www.eeoc.gov/facts/ada17.html An individual with a disability must also be qualified to perform the essential functions of the job with or without reasonable accommodation, in order to be protected by the ADA. This means that the applicant or employee must:
satisfy your job requirements for educational background, employment experience, skills, licenses, and any other qualification standards that are job related; and
be able to perform those tasks that are essential to the job, with or without reasonable accommodation.
The ADA does not interfere with your right to hire the best qualified applicant. Nor does the ADA impose any affirmative action obligations. The ADA simply prohibits you from discriminating against a qualified applicant or employee because of her disability.
Here's what the ADA says about accommodations in college:
What are academic adjustments and auxiliary aids and services?
Academic adjustments are defined in the Section 504 regulations at 34 C.F.R. § 104.44(a) as:
[S]uch modifications to [the] academic requirements as are necessary to ensure that such requirements do not discriminate or have the effect of discriminating, on the basis of [disability] against a qualified ... applicant or student [with a disability]. Academic requirements that the recipient can demonstrate are essential to the instruction being pursued by such student or to any directly related licensing requirement will not be regarded as discriminatory within the meaning of this section. Modifications may include changes in the length of time permitted for the completion of degree requirements, substitution of specific courses required for the completion of degree requirements, and adaptation of the manner in which specific courses are conducted.
Here's the link for the full text:
http://www2.ed.gov/about/offices/list/ocr/transitionguide.html 
