Well at the law firm I worked at, they had Data Entry Clerks that entered data into Access Forms, or directly into the tables. The Developers did the Database Administration for them. That was my job, import data from another source, update the queries, fix the reports and forms, etc. I got paid way more than $7/hr for that, more like $24/hr for Programming, Database Administration, Tech Support, Documenting of Applications, Report Writing (Database based Reports in Access and Crystal Reports), and other misc things that always came up like training people, etc.
The problem as I see it, companies don't want to pay someone $24/hr anymore and would rather have the entry level people do some of the same tasks for a much lower pay. So they give some of the Developer or Database Administrator duties to the entry level people. That way they can eliminate the $24/hr position. Some companies are offshoring the jobs elsewhere were people in other countries can do the job for pennies on the dollar, or replaced by H1B Visa workers earning about as much as you are or a little bit more.
All I can say is that if it is raising red flags for you on stress, you might want to consider a different job. Learn Access anyway, at least it can give you a good idea on how Databases work and you can work a job with Access in the future some time.
I have worked jobs where I was given time to learn the new technologies. In 1994 I was handed a shrink wrapped box of Access 1.0 and was told to learn it, or else. So I installed it, started reading the manual, and made a few sample databases, much like the one I had you made to teach you a simple example. Sure I was afraid that I might not be able to learn it in time, but I learned it and was able to build my skills and get pay raises. I co-developed a Technical Problem tracker with a coworker and we were able to fix problems faster, keep track of them, and email our bosses a report each week. I even made a Network Management database for the Network Administrator so he wouldn't assign duplicate addresses to different boxes. No more network configuration issues, except when Engineering copied an existing hard drive to another one and created dupes on the network, that was fun to track down. :)
I also dove into Oracle in 1996 with a Federal Contract job for the US Army, picked up some Unix skills too. I found that it was easier to learn since I knew SQL from Access and other databases like SQL Server that PL/SQL was easier to learn because of that.
At the Law Firm I had to learn ASP and Crystal Reports, I aced those.
Always learn something new as technology keeps on changing.
Remember that sometimes you don't always have to take the first job offered to you. Learn from it and maybe the next few jobs will be more appealing. Maybe you can ask for $8 or $9 an hour at your next job interview, and maybe they can offer a 20 hour work week and Data Entry without DBA work.