An agency services a family with two elderly people who need care, but only pays the aides for one person service. Is this fair?

What does your agency say about this? This would be highly unusual, because they may want to claim that you are being paid "by the hour" and that you therefore will do what you "can" do in that time. That said, the elders would be getting one half the care they would get were there only one needing care, if you see what I mean. For instance, my pay as an RN was by the hour. How many patients they put upon me, and how well I could do for those patients, depended upon how much time I could devote to each of them. When Schwartzenegger was our Gov. in California he put a limit on how many patients an RN would have to care for, dependent on shift worked.
Interesting questions, this.

If you are the caregiver and are getting paid you do the work that is required for that particular client.
It is up to the Agency to establish a contract and bill the clients appropriately. If the Agency is unaware that there are 2 people that need care then it should be brought to the attention of your supervisor.
If this has been a slow process and one as begun to need care and did not previously that also should be brought to the attention of a supervisor.
If you think that caring for 2 people is more than you can handle then inform your supervisor that caring for 2 people is more than you can handle and ask to be transferred to another client. If you think it is unsafe for 1 person to care for this couple that should also be brought to the attention of your supervisor along with the request to be taken off this clients schedule as it is unsafe in your opinion.

I don't understand why people get mad about having to work hard when they are getting paid for their time.

No back pay if you agree to the wage and job description.

My experience with a reputable agency *as a client* was that we were billed for 2 people being cared for by 1 aid. Each client had to pay, but this was our contract agreement with them up front. I had no insight into what the aid was actually being paid by the agency. Did the employees sign a contract with the agency? I would start by reading that...