So how would one have a clean "partial backup" strategy if something similar would happen in his company?
Depends a lot on the situation and technologies already in use. For example, if you lost ticket sales, you might monkey patch it by having two systems at the entrance: one with the main data, one with the restored backup. If the person isn't in main, you can check backup. That could be deployed more quickly than trying to consolidate the two states.
In another situation, you could isolate customers so that a delete and a restore simply affects everything at that customer and such a partial delete is not a problem. You could still have trouble if there is a partial delete within a customer system, but restoring part of 1 company is a lot less work than restoring parts of hundreds of companies.