A user on Reddit shared this file (and I also downloaded myself from Microsoft alternatively, so I could verify that his file is legit). Since the forum administrator bans sharing a link, I'm not including the link to the post, so you can search for "Windows 10 Recovery Image for Surface Pro 3" on surface subreddit. However I didn't have any luck using this image to get a pure SP3.
My SP3 is clean installed 10240 then upgraded to 10586.11 via Windows Update. However, after trying to use the recovery flash drive, the windows version was still 10586, not 10240. No pen paring step during the initial setup, nor the Surface logo in Computer Properties page. Somehow the recovery wizard did not read from the flash drive, but used the files stored in the device's SSD to perform the reset....
Any ideas?