Hi,
I'm sorry, but this is completely innacurate. I don't know where you got that information from, but I would not trust that source anymore

f-numbers are a ratio of actual aperture and focal length. So an f-number of f/4 on a DSLR will be the exact same thing as an f-number of f/4 on a point-and-shoot. The whole POINT of f-numbers is to allow comparison of lenses with different physical dimensions.
For instance, if you consider the lens of the Canon S2 (or S3, or S5, they're the same lenses) you will see that its maximum focal length is 72 mm (not effective focal length, mind you, I'm talking about the
real one). Considering the smallest f-number possible (largest aperture) of f/3,5, that means the physical aperture is at most 20,5 mm. Now, consider a lens with a focal length of 200 mm and an aperture of 57 mm. That's a much larger lens by all accounts. Yet it has an f-number of... f/3,5.
I believe that what you meant is that the depth of field of a point-and-shoot is different than that of a DSLR. In that case you are both correct and wrong.
The problem is that point-and-shoot sensors are much smaller than DSLR sensors (which are usually smaller than film). So manufacturers advertize "effective" focal lengths to give you a film equivalent, which most people are familiar with. So, keeping in mind the lens of the S2, it's "effective" focal length is at most 432 mm. Its REAL focal length remains 72 mm, though, that's the physical distance betwen the lens and its focal point.
And any lenses with a 72 mm focal length and an f-number of f/3,5 will give you exactlty the same IDENTICAL depth of field.
I hope this helps clarify things a bit. Feel free to ask questions if you have more, I want to make sure what I wrote is clear, as it's not an easy topic at all.