Yes, the problem could have been made uninteresting by removing any
ambiguity. But as stated, it is very common (almost universal) to
speak of movement of a terrestrial object with respect to the surface
of the earth. If another frame of reference is intended, it is almost
always specified. Two movements are mentioned in the problem. Is
there any reason to suspect that one is movement relative to surface
of the earth (the conveyor) and the other is movement relative to the
first object? Why not th other way around, in which case the conveyor
is just an ordinary runway?

If you are not willing to resolve that ambiguity by assuming
conventional frames of reference, you might as well assume that one is
speaking of velocities relative to a solar system frame, in which case
the plane may be going very very fast forward, backward, sideways, up,
or down, depending on time of day and orientation relative to the
earth. The problem makes a lot more sense assuming conventional use
of "moving".

Yes, the frame of reference has everything to do with the answer ...and the
riddle!
Since the original post refers to an airplane taking off you should conclude
that
"air" (the atmosphere) has to be included in the mix and that an airplane
does it's
flying relative to the world/atmosphere. Then it is not unreasonable to
assume that the riddle
implies that the most logical reference frame is the planet and that the
conveyor and the plane
are moving in opposite directions with respect to that stationary observer.
The only requirement
then is that the airplane move fast enough to take off and that the conveyor
move fast enough "backwards"
to match the airplanes speed (only to satisfy the specified initial
conditions even though the speed of
the conveyor is entirely irrelevant to whether or not the airplane takes
off.) It doesn't even matter if the wheels
need a bearing job or if the plane is on skids or if the brakes are set.
Either the engine generates enough thrust
to overcome resistance and accelerate the plane to take off or it doesn't.