> Should we presume that it must be an invisible ball of matter that gravitates but we have no other way of detecting except through the same effect we use to infer its existence, or should we tweak Newton's laws of physics?

"we have no other way of detecting except through the same effect we use to infer its existence" is true of everything in the universe. We believe stars exist because we can see the light coming from them, but light is our only way of detecting them.

There's no single answer to this kind of question, we have to actually do science and make observations. We should ask whether it behaves like a ball of matter (e.g. does it have a point location in space? Does it orbit the way a ball of batter does?) or like a modified law of gravity (can we reproduce the same conditions)?

The likes of the Bullet Cluster makes a very compelling case that cold dark matter is real.