Nope. DisplayPort can adapt to HDMI or DVI passively. It won’t support the proprietary bullshit like HDCP, but it will be able to display video just fine. Pin 13 on DP is specifically used to detect adapters, so the output device can automatically change to using an HDMI protocol if it detects an HDMI adapter. This technically requires a dual-mode DP port to automatically adapt, but the vast majority of DP connectors produced in the past several years are dual-mode.
But going the other direction (HDMI to DP) requires an active adapter, to strip out all of the proprietary HDMI-only bullshit.