If this is true, secure wiping of SSDs would be very difficult if done using software.
As always, the best practise is to simply encrypt the files right from the start of it's creation rather than half-ass effort of encrypting the files a while later when some backup copies or temp copies start to spread all over your system. Even better, setup an encrypted filesystem right from the start so that your files would be transparently encrypted without you needing to select every single file to be encrypted.
Anyway, software-based secure wiping have never been proven to be specifically secure because the software MUST depend on the OS level to do the 'FSYNC' methods or write methods onto the hardware and each hardware have their unique quirks too nonetheless.
To truely be secure in the destruction of the data on your hard disk, you need to destroy it physically by structurally rendering it impossible to be repaired and recovered anymore.
For the usual circular hard disks, magnets (strong rare earth magnets or very strong electro-magnets ) may possibly wipe and skewer the data bits but the best way is to take a sharp objects and randomly and tightly scratch each side of the circular plates. Another way is to toss it into fire, thermite it, shoot it multiple times with a 12 guage shot gun... whatever ways that would physically render the hardware irrecoverable.
For flash based (USB devices, SSD, flash memory) , you do have to short circuit the chips with high voltages. Then finally, you may want to be more thorough by using fire or thermite. Maybe using a chisel and / or a hammer that is heavy enough to turn it into brittle fragments would be useful too.
All in all, software based wiping seems to be less useful these days and the better things are to physically turn the hardware into some irrecoverable hardware.
Have fun using thermite on your data storage hardwares. :D