Is this accurate? It's actually easy to check - here's the math (I used Google to get equatorial diameters of the Earth and Moon diameters and regulation sizes for the balls):
Diameter of the Earth = 12,756 km
Diameter of the Moon = 3,476 km
Ratio of Earth/Moon = 3.7
Diameter of Basketball = 9.4 in
Diameter of Tennis Ball = 2.6 in
Ratio of Basketball/Tennis Ball = 3.6
Not exact, but close enough and a useful comparison because everyone can visualize the sizes of a tennis ball and a basketball.
How about distances? Well, the orbit's an ellipse so we can can only specify an average distance which is about 384,403 km. Let's scale this distance to the average of the scale we have for the Earth and the basketball (we could also have used the Moon and the tennis ball). Here are the ratios:
(Scaled Earth-Moon distance in inches / 384,403 km) = (9.4 in / 12,756 km)
Scaled Earth-Moon distance = [(9.4 in) (384,403 km) / 12,756 km]
Scaled Earth-Moon distance = 283 in (rounded off) = 23.5 ft
As the video showed, that's a lot further than most people would have estimated!
How big would the Sun be on this same scale? The diameter of the Sun is 1,392,000 km. Once again, we'll set up a ratio scaling to the same ratio as the Earth and basketball.
(Scaled diameter of Sun in inches / 1,392,000 km) = (9.4 in / 12,756 km)
Scaled diameter of Sun = (9.4 in) (1,392,000 km) / 12,756 km
Scaled diameter of Sun = 1026 in (rounded off) = 85.5 ft
If the Earth were the size of a basketball, the Sun would be the size of two school buses parked end-to-end! The size of a very large house.
How far away would it be? As with the Moon orbiting the Earth, the Earth orbits the Sun in an ellipse so we'll use the average distance of 149,597,871 km:
(Scaled Earth-Sun distance in inches / 149,597,871 km) = (9.4 in / 12,756 km)
Scaled Earth-Moon distance = [(9.4 in) (149,597,871 km) / 12,756 km]
Scaled Earth-Moon distance = 110,240 in (rounded off) = 9,187 ft = 1.7 miles
So, if the Earth were the size of a basketball, the Sun would be 1.7 miles away!
How far away would the nearest star be? Proxima Centauri is 3.97 x 10^13 km away.
(Scaled Earth-Proxima Centauri distance in inches / 3.97 x 10^13 km) = (9.4 in / 12,756 km)
Scaled Earth-Moon distance = [(9.4 in) (3.97 x 10^13 km) / 12,756 km]
Scaled Earth-Moon distance = 29,255,252,430 in (rounded off) = 461,730 mi
That's almost twice the distance from the Earth to the Moon! So, if the Earth were the size of a basketball, the nearest star would be twice as far away from it than the real Moon is from the Earth.
And these are just our closest neighbors. Everything else is orders of magnitude further away. The universe is a very, very big place.