They do all broadcast in HD but the problem is from a regulatory and legal point of view HD is simply a matter of resolution. The SKY HD offering was well known and discussed at length on the AVF well before it launched and a search back to early 2006 may make interesting reading for you, or not
To put simply if channels had to be 100% native HD there would be far less HD growth and takeup, perhaps some channels we have now would not have bothered and we would also lose the obvious benefit of broadcast HD from SD masters not domestic upscaled HD from crippled SD broadcasts.
Long term yes more native HD but in practical terms I prefer the full simulcast channels with an ever growing percentage of HD compared to the BBC, ITV and even FXHD's. Disco and the other docs are 100% native but again very repeat dependent to fill both a fulltime and part time schedule.
Eurosport HD unlike others have a permentant HD tag to differentiate it from the other Eurosport output, when it's native HD they add the onscreen FullHD tag and HD in the EPG.