Is a DJ a Musician?

I saw a DJ perform a few weekends ago and he was extremely talented at what he does. At this time I had not seen very much work from djs but knew enough about it to see that what he was doing was difficult.
Many people say “Djs are just people with no musical talent, that is why they use other peoples music to create their own mixes.” But I have to disagree with that because although yes, they are not using their own music, but they are mixing them together to make a seamless gap between them or creating remixes of the songs, taking one beat from one song and mixing it with the bass and singing of another. People that tell me that it takes no talent to do that obviously have not experienced DJing and therefore cannot appreciate it.
As someone that has just started to dabble with DJing, I can tell you that it does require a certain amount of musical talent. A DJ has to interoperate the music he is mixing, by knowing the BPM or the key of the song. Where certain parts of the songs are similar to others and they also have to be able to read a beat. A dj that cannot predict where anther beat can be placed or a key that can be changed is going to struggle with his mixing.
Also people that say that DJs have no musical talent have only heard the work of some DJs, what about Tiesto who makes a lot of his music over the top of classical music, or Armin van Buuren who makes a lot of his own music to mix. Look at the top 10 djs in the world, many if not all make and use their own music in their mixes.
If that does not show some musical talent I don’t know what does.