As of June 2019, can a DPE in the United States renew a CFI's certificate based on completion of a FIRC? Flight instructors need to renew their CFI certificates every 24 months. One of the ways to do that is by completing a FIRC. In the past, you had to take your completed FIRC to the local FSDO and have an inspector approve it. 

Lately, I've heard rumors that FSDOs are so overworked that they're not doing CFI renewals any more, and are sending them to DPEs instead. 

Is this rumor true? Can I take a completed FIRC to a DPE in June 2019 and re-up my certificate?
Yes they can
I asked a DPE to renew mine a couple days ago and they did.  Sometimes asking nicely is the best way to learn.