I dug out one of my old Cores, and I am getting the same results you are. DHT.acquiring() always returns true, so it never makes it past that test. I tried powering it from 3v3 and from Vin, with and without a 1k pullup resistor on the data line (it works without that on the Photon, but I’ve seen some tutorials that use it, and others that do not).
After Edit: I compiled against 0.6.0 (above), then I tried 0.5.3 and 0.4.9. It finally worked with 0.4.9. The PietteTech library uses interrupts, and there is a known issue with interrupts and the Core in firmware versions 0.5.3 and up. See this link.