At those speeds and slip of the narrow wheels that's manageable. With a lot of weight on it it would be more problematic. At least now when on slippery surfaces you have some traction, a limited slip differential would be tricky to make cheaply and would consume quite a bit of energy. A normal diff would cause you to get stuck very quickly.

He said so and it does seem to have solid axle and it only shows it driving on dirt and grass.

One way to solve it would be to have only single wheel powered. If you get that one powered wheel lifted you could shift your weight to tip entire vehicle (assuming you took care to load it evenly).

Or just use a limited slip diff. Allows some slip for cornering, but only, well, a LIMITED amount you don't end up with one wheel in the air spinning like mad and the one with traction not moving at all.