Unless someone figures out how to register a domain ending in ‘.com|disabled’ I’m not sure how someone would be able to access those accounts.
I believe it's easy to spoof emails from the .com|disabled domain. Receiving messages, I agree, seems harder. Maybe spoof an unencrypted DNS response at the right moment? No need to actually register a domain when DNS is spoofable.[1]
If you really need to use a hack like that to disable an email, consider adding some code to your email sending logic that skips such email addresses (and always use that logic). Otherwise clever hackers have a foothold to try their tricks against.
A lot of people are complaining about NYT approach, but perhaps their only fault - if one consider that not deleting for good an account is not an issue, and it seems to be a common practice in the industry - is to not use a transaction when disabling user accounts (disable email -> disable account), which is perhaps difficult with NoSQL setups?
DNS is a very old protocol that still has lots of problems and mitigations like DNSSEC are only partially deployed.