Hi Sapphire,
Welcome - sorry it's a sad first question
Some thoughts for you to ponder; they may help you decide how to proceed, assuming you're not already beyond the point of no return ...
Have you any way of validating what this person has said - anyone else to speak to? The owner of the site, or other tenants? You need to make sure he's not mistaken before you make any decisions.
Can you get onto the plot to investigate? Is the problem across the whole plot or just in bits?
Did the plot previously get given up because it wasn't cultivatable? If so, it's a cheek to try to force you to take it now.
I note what you say that this is the only plot available, but does that mean that's the only one free now, or the only one you will ever ever ever get offered?
If you turn down this plot, will you get offered any further plots if and when they eventually come free? Or do you just go down to the bottom of the list immediately (or are even taken off the list)? On my site, you get three offers and then you're back to the bottom of the list.
Any idea how long the waiting list would be for a better plot?
If it truly isn't cultivatable and you would eventually get offered another plot, it might well be worth sacrificing your understandable keenness to get started now, and wait for something which will produce proper crops.
If you have to keep the plot, you could increase the growing depth by making raised beds but that can be expensive, particularly if you need to import soil. Add lots of organic matter etc to improve the soil.
Others, I am sure, will have other ideas too.