Usually they reference a government document that says that physical destruction of the media is the only correct method to erase TOP SECRET (and above) data, but that is mostly paranoid burocracy.
If you're using a SDD however, you have to deal with firmware wear-leveling, garbage collection and the drive having a lot of GBs hidden from everyone, even the OS. There are some proposed techniques to force an unavailable block back into the available pool and then reading long-deleted data. Afaik, there's little you can do in this scenario, even full disk encryption might not help you with the old data blocks that are still waiting to be zeroed by the GC.
Then again, like you said, FDE is probably the easiest way. TrueCrypt was vulnerable to some on-memory-key attacks, but for data killing its more than enough. There are some projects that have forked TCs code, and there also the old version available thats still fully functional.
https://ata.wiki.kernel.org/index.php/ATA_Secure_Erase
If you have a linux box handy, you can probe your ATA-compatible drives with:
root# hdparm -I /dev/X
look for: Security:
Master password revision code = 65534
supported
enabled
not locked
not frozen
not expired: security count
supported: enhanced erase
Security level high
2min for SECURITY ERASE UNIT. 2min for ENHANCED SECURITY ERASE UNIT.
"Enhanced Security Erase Unit" should get all of the sectors that have been previously used even on a SSD with wear leveling.Of course, you still have to trust that the vendor has correctly implemented it. I have no idea what best practices are in that regard. If anybody here has a better idea, I'd love to hear (Is FIPS certification a good sign? If the drive implements encryption and can therefore do a secure erase by dropping the keys can it be trusted? Can drive vendors generally trusted to not use ECB mode? etc.)