First, it's not uncommon for virtual disk formats to be logically zeroed even when they are physically not. For example, when you create a sparse virtual disk and it appears to be XGB all zeroed and ready to use. Of course, it's not. And this doesn't just apply to virtual disks, such techniques are also used by operating systems when freeing pages of memory - when a page of memory is no longer being used, why zero it right away? Delaying activities until necessary is common and typically built in. Linux does this, Windows does it [http://stackoverflow.com/questions/18385556/does-windows-cle...], and even SSDs do it under the hood. For virtual hard disk technology, Hyper-V VHDs do it, VMWare VMDKs do it, sparse KVM disk image files do it. Zeroed data is the default, the expectation for most platforms. Protected, virtual memory based operating systems will never serve your process data from other processes even if they wait until the last possible moment. AWS will never serve you other customer's data, Azure won't, and none of the major hypervisors will default to it. The exception to this is when a whole disk or logical device is assigned to a VM, in which case it's usually used verbatim.
This brings me to the second issue. Because using a logical device may be what DigitalOcean is doing, it's been asked if it's hard for them to fix it. To answer that in a word: No. In a slightly longer word: BLKDISCARD. Or for Windows and Mac OS X users, TRIM. It takes seconds to execute TRIM commands on hundreds of gigabytes of data because, at a low level, the operating system is telling the SSD "everything between LBA X and LBA X+Y is garbage." Trimming even an SSD with a heavily fragmented filesystem takes only a matter of seconds because the commands to send to the firmware of the SSD are very simple, very low bandwidth. The SSD firmware then marks those pages as "free" and will typically defer zeroing them until use. Not only should DigitalOcean be doing this to protect customer data, but they should be doing it to ensure the longevity of their SSDs. Zeroing an SSD is a costly behavior that, if not detected by the firmware, will harm the longevity of the SSD by dirtying its internal pages and its page cache. Not to mention the performance impact for any other VMs that could be resident on the same hardware as the host has to send 10s of gigabytes of zeroes to the physical device.
Not only is DigitalOcean sacrificing the safety of user's data, but they're harming the longevity of their SSDs by failing to properly run TRIM commands to clean up after their users. It hurts their reputation to have blog posts like this go up, and it hurts their bottom line when they misuse their hardware.
Edit: As RWG points out, not all SSDs will read zeroes after a TRIM command, so other techniques may be necessary to ensure the safety of customer data.