Would have to disagree with that, I've found my Classic (with ARB) handles very well even when pushing on. It feels much more secure than either a P38 or L322 on air both of which I found to wallow in the corners more than a coil sprung Classic. I would say though it will be interesting to compare my '91 on coils against the '93 LSE on air (when I get it finished).
To the OP, the pictures suggest to me that Rangie has been lifted and off roaded so not a total surprise it wallows and jiggles around a bit. According to the info in the notorious Haynes manual, anti roll bars were introduced in December 1990, so yours may not have had them, but then lifting it would make it roll even more in the corners.