I have discovered that this issue has been discussed quite a bit in the Reaper community. I'm pretty sure they are describing the same problem. They attribute it to how the software deals with signals from triple sensor keyboards.

Here are some extracts:

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Consider this MIDI sequence:

TIMESTAMP IN PORT STATUS DATA1 DATA2 CHAN NOTE EVENT
146543542 1 3 144 60 95 1 C 4 Note On
146543812 1 3 144 60 95 1 C 4 Note On
146544096 1 3 144 60 95 1 C 4 Note On
146545843 1 3 144 62 91 1 D 4 Note On
146545972 1 3 144 60 0 1 C 4 Note Off
146545972 1 3 144 62 0 1 D 4 Note Off
146546288 1 3 144 62 91 1 D 4 Note On
146546442 1 3 144 60 0 1 C 4 Note Off
146546442 1 3 144 62 0 1 D 4 Note Off
146546823 1 3 144 62 87 1 D 4 Note On
146547009 1 3 144 60 0 1 C 4 Note Off
146547009 1 3 144 62 0 1 D 4 Note Off
...

The problem is, modern piano keyboards that use a three sensor technology will produce these sequences when a key is stroken and thereafter not fully released, but only half-released and stroken again.
This behaviour mimics the repetition behaviour of a real Grand Piano.
...
Yamaha Digitals and Hybrids like GT2, Avant Grand and all Clavinovas with GH3 keyboards can produce such sequences.
Roland PHA III keyboards /should/ do it. Casio Tri sensor keyboards do it definitely, this are almost all recent piano models from Casio.
...
When I play from my Kawai MP7 to a hardware synth via Reaper, I can have the same note overlapped ...If I use another controller I don't have the problem. ...
MP7 has a triple-sensor keybed action, this is a pretty normal thing then, because you can start a new event before the first one has finished.
...
Triple sensor actions can and will create stuff like that, because you can trigger another note before the first one receives a note off (because of the third sensor placed in between the main two ones that all the other regular actions have).
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Extracted from discussions on this forum:
https://forum.cockos.com

Ed