The jump was made.
The apparent curvature is a combination of effects.
1. Optical illusion. An expansive horizon appears to curve to our eyes. Even in RET, a commercial aircraft never reaches an altitude to allow you to perceive a spherical earth's curvature - yet people claim to see this all the time. Our eyes play tricks on us.
2. Wide-angle lens. As above, this enhances the effect. The image is a little distorted even at lower altitudes.
3. At very high altitudes, looking out along the edge of a disc will produce - you guessed it - a curve.
I don't think Red Bull intentionally swapped lenses or faked any of this. I believe the flight and jump were genuine - but it didn't get high enough to perceive the true nature of the earth as a disc. Sub-orbital flights are not only possible, but rather routine, and they do reveal a breathtaking view of our earth, but not a global panorama - even if it were a sphere.