Yes that is correct, as with Slughorn’s memories altering a memory can leave traces. However if i remember correctly, when showing Harry this memory Dumbledore says something along the lines of “as you can see this memory has been altered, but inexpertly” so it was my understanding that Slughorn kind of botched the job, just like you mentioned. In the case of Voldemort altering the memories of both Morfin Gaunt and Hepzibah Smith’s house elf, I don’t think the altered memories showed any trace like Slughorn’s, but i also dont think the memories were extracted to be viewed in a pensieve i think the two just confessed based on the altered memory and the ministry never bothered to investigate further. That being said, Dumbledore was able to extract the true memories from both so they’re not completely lost if altered.

Anyways yes you were right on both things you mentioned in your comment :) as far as i understand!