If you look at the definition of DbSet<TEntity>:
public class DbSet<TEntity> : DbQuery<TEntity>, IDbSet<TEntity>, IQueryable<TEntity>, IEnumerable<TEntity>, IQueryable, IEnumerable, IInternalSetAdapter
where TEntity : class
Because it has a type constraint that the generic type must be a class then you must initialize it with a type that also matches this condition:
public class GenericRecordController<T> : Controller where T : class
{ ... }