Turns out I don't have sufficient privileges to close this (my own) issue. So can please someone close this for being a duplicate?
Oh yes, you're right. I did not find this one.
I just verified that the bug is still present in the current 3.8.1 release. There are additional details in the duplicate issue 1283 for 3.7.1.
Copy as SQL INSERT-VALUES replaces table name with "PressCtrlH"