If you are defining music from a process-based view, without talking at all about the actual musical forms, then lots (not all) music falls into the folk music definition. Rap, for instance, is more folky in some ways than most folk songs. However, when talking about musical genres, it makes a lot more sense to talk about what makes a genre separate from another genre. If you really think all music is folk music, that it's the playing it with others that makes it folk, why come to a folk music site? Also, why start discussions like this? Why bother calling it folk? Why not just call it music?

For my own purposes, I tend to define folk music by musical attributes rather than seeing it as part of a tradition or as an example of a process. But here's where the process comes in: traditional music is, by and large, music that has passed through a specific process or is music that sounds so much like the traditional stuff that it doesn't matter in the real world. Thus, rap is defined by largely non-melodic lyrics and a strong dance rhythm. For the purpose of any meaningful discussion of what we like, it's not folk music. Country music, broadly, is mostly two or three chord songs with relatively simplistic melodies. Singer-songwriter music is music that is composed by singer-songwriters. They all tend to sound different than each other, and different than traditional music.

That said, one of my favorite things is to find the similarities between different types of music and play to them. Given that I like traditional music the most, this usually happens with different traditions rather than different genres, but the idea is the same. There are strong similarities in my mind between medieval music, French traditional music, and the blues. I think traditional folk mixes with rock music better than with jazz because rock music and traditional music both tend to sound good with diatonic scales and open (no 3rds) chords. Jazz usually has more chromaticism and more complex chords and chord structures, making it more of a stretch to play folk music in a jazz style.

A definition based on musical style is easier to deal with if we are talking about what we like to listen to and play. Rap as folk music might be interesting to an academic as an academic question, but for a musician and a consumer of music it really has very little value.

Are you really saying you can't hear the difference between traditional music and non-traditional music?