HDMI can be thought of as a mere pipe that can send any kind of data (encoded, uncompressed, etc) from device to device. One example is that it sends compressed Dolby & DTS formats along just fine. The ability of using it to record is purely a matter of the content protection assigned to the content itself. I have seen, for example, a PC card that has a HDMI input for performing capture, so it is technically possible for non-protected content. Certainly it would be better to do this with compressed content due to the need to record at a reasonable bitrate to accommodate the storage media.
However, I have seen no indication that HDMI will be used in this manner in any mainstream products in the near future, and it appears that uncompressed video will be the format used for HDMI for a while.