Funny you should ask that. I have just been trying to cut 0.8 mm Ti 6Al4V sheet on a fine-toothed bandsaw. Lots of noise, and regular bangs and sparks. But I strongly suspect the sparks are individual steel teeth coming off the blade, as they have hit me in the face a few times. Yes, safety glasses. In the end, I gave up and went a very different route.
So while I have seen sparks while machining Ti, I don't think they were from the Ti. More likely from ... a mistake.
However, I have also generated a lot of fine titanium shavings in the workshop - long spirals etc, from machining. Just as you can light a thin ribbon of magnesium with a hot flame, so you CAN light a shaving of Ti. Both burn with a spectacularly bright and fast flame. (The usual caution: don't try this at home ...)
However, I very seriously doubt you would ever get titanium to burn while you were machining it (assuming a modicum of common sense). You would have to get it more than red hot, and if you do that the tools you are using will die very fast. Machining Ti is best done with a very sharp edge, a slow speed, much coolth and moderately aggressive cut.
Sparking of a Ti tent stake? Never seen it, but with something as hard as granite it appears to be possible. Chance of lighting a fire? Doubtful imho. The Ti particles would have to be very small, with very little energy content. I think.