You are getting a bum steer from whoever told you this.
Sea grass has nothing to do with swimming. It is correct that the sea grass is not cut on Ambergris Caye. This is to prevent the island from blowing away during the next hurricane. There are sandy areas here and there in the shallows but usually grass in most areas right along the shore.
It means that in most places you will probably want to wear little dive booties or stockings if you insist on walking into the water from the beach. (It depends on how sensitive your feet are....)
Or you can do what most people do, which is to jump (or go down the steps) on the piers into the water.
The water is clear, warm and delightful and the grass at the bottom has nothing to do with swimming. There are plenty of sandy areas in the low wake zone interspersed with grassy areas on the ocean floor (and you can see fish, grass or not!)
Susan Guberman-Garcia, Attorney at Law. Phone: 510-792-2639
Fax/Voicemail:: 510-405-2016 Email: firstname.lastname@example.org