But still cannot explain why in zoom mode it shows the correct signal...
The megazoom chipset has two memories. One is the acquisition memory and the other is the measurement/display memory.
When you capture a signal it all goes into the acquisition memory at whatever rate the scope needs to fill more than 10 divisions, up to the maximum rate. This rate is calculated automatically and is displayed on the right hand menu bar (at least on the 3000).
The acquisition memory is then processed with averaging and placed into the measurement memory memory which is further processed for the display. The measurement memory, according to the manual, is at most 62500 points for the 3000, but I think you're right it's 16k by default.
So, each data point in the measurement memory is a result of averaging some number of acquisition points. As you zoom out you're effectively averaging more points of the sine wave per measurement/display point and the amplitude will approach zero.
In split screen mode it's computing the display twice, once for the top zoom and once for the bottom zoom, but still using the same acquisition record for both. When you zoom in on the bottom waveform, the scope is doing the same operation as in non-split screen mode and it computes the average using less acquisition points per display point and you get your amplitude and signal detail back.
You can also see this effect with a single-shot capture.
Hope this clears it up a bit.
I generally don't use averaging unless I have a few cycles of a waveform on the screen that I need to clean up. High resolution mode has similar side effects, but doesn't need a repetitive waveform, so I usually choose that to reduce noise.