Drive manufacturers don't have to indicate HTL support. It is the defaut. I am telling you from a historical perspective that it is a fact that every. single. BDRE. drive. will "handle" HTL media. Most media IS HTL.
To that end, every single popular disc model is adequately supported in any new drive you can get. No exemptions. Whether or not the particular media a person gets is good, that's debatable. Whether or not a drive has bugs (see also: Samsung SE-506CB), that's independent of the fact that the support is still there.
With any BDRE drive from the past 3 years, you have inherent support. It is implied. If you got an old drive, the only one you would have to even remotely worry about is LTH, but even LiteOn made its best attempt to get decent write quality on its iHBS112/212/312 drives before ending production.
Note that we are at the point that drive manufacturers shouldn't have to specify LTH support; it's strictly a matter of if a write strategy exists for whatever disc model you want to use. And with single layer or double layer BD media? Things are mature enough that support will be there. For triple layer media, some people have had issues with Sony triple layer media, but the other popular TL media is supported, and newer drives/new firmware helped resolve some of those incompatiblity issues.