The existing answers are mostly correct, but I wanted to provide some additional information confirming this.
tl;dr: They are correct that the relevant federal labor laws don't apply to them due to the size of their business, but what they did would be permissible even if they did.
The primary applicable law in the U.S. is the Americans with Disabilities Act (ADA).
Applicability to Small Businesses
You say that the employer has less than ten employees. As it turns out, they're actually correct that ADA does not apply to them. The primary applicable part of the ADA is 42 USC 12112(a), which says:
No covered entity shall discriminate against a qualified individual on the basis of disability in regard to job application procedures, the hiring, advancement, or discharge of employees, employee compensation, job training, and other terms, conditions, and privileges of employment.
Initially, it sounds like this might apply, but, as with all laws, definitions of terms are important. 42 USC 12111 defines the terms applicable here. Of particular importance are (2) ("Covered Entity") and (5)(A) ("Employer"):
(2) Covered entity
The term “covered entity” means an employer, employment agency, labor organization, or joint labor-management committee.
(A) In general
The term “employer” means a person engaged in an industry affecting commerce who has 15 or more employees for each working day in each of 20 or more calendar weeks in the current or preceding calendar year, and any agent of such person, except that, for two years following the effective date of this subchapter, an employer means a person engaged in an industry affecting commerce who has 25 or more employees for each working day in each of 20 or more calendar weeks in the current or preceding year, and any agent of such person.
So, indeed, ADA is not applicable to this employer if they have fewer than 10 employees. They would need to have 15 or more before ADA protection kicks in. This is largely because, while something might be considered a minor responsibility that could just be covered by someone else in a large organization, that isn't necessarily the case for a small business with only a few employees.
(As a side note, "person" under U.S. law does include corporations, so the definition of "employer" does not exclude corporate employers. Though they would indeed be excluded from ADA requirements if that were not the case.)
Who is a "Qualified Individual"?
While ADA is completely non-applicable to the employer in this case, even if it were applicable, the next question to be answered would be, "Who is a 'qualified individual?'" Of course, the law answers that, too:
(8) Qualified individual
The term “qualified individual” means an individual who, with or without reasonable accommodation, can perform the essential functions of the employment position that such individual holds or desires. For the purposes of this subchapter, consideration shall be given to the employer’s judgment as to what functions of a job are essential, and if an employer has prepared a written description before advertising or interviewing applicants for the job, this description shall be considered evidence of the essential functions of the job.
So, if you have a disability that renders you unable to perform one or more of the essential functions of a job, even with reasonable accommodations, then you are not considered to be a "qualified individual" with regards to that job for purposes of ADA protection. Which, of course, makes sense. You wouldn't want to hire someone as a baggage handler or a carpenter if they couldn't lift heavy stuff, for example.
Additionally, note the language in the second sentence. First of all, it's mostly up to the employer (within reason at a court's discretion) to determine what is considered an "essential function" of a given job. Second, if an employer has prepared a written description of the position before advertising or interviewing candidates for it, then that's considered evidence of the essential functions. That's one reason why it's important for employers to have the sort of description you quoted in the question. If a case were to go to court (and the case weren't dismissed for inapplicability of ADA to that employer,) then that job description stating up front physically demanding aspects of the job would be considered evidence in favor of the employer.