Banjo, you are right! You and I know about newest technology about closed-captioning. There is no closed-captioning through HDMI video, period. 
P.S.: I have HDTV with DVD upscaling have HDMI output, and it don't have closed captioning. Best bet that I recommend you, if you want
to choose movies that have English SDH (subtitles for the deaf and hard-of-hearing instead CC, you can choose by movie are produced and distributed, here list for Hollywood studios:
Warner Bros (since July 2007) - not bad SDH but sometimes there would be no lyrics during singing or title song.
Universal Studios - Best SDH around this DVD!
Walt Disney (it still be closed captioned as long as well they don't have logo for CC, just only SDH since 2005 on rear artwork of those DVD.)
Weinstein Company
Recently, I saw on those newer DVD releases from Anchor Bay was just begun stating SDH, but I haven't watching so I couldn't test it until I have
watching it, I will review about Anchor Bay for all people who read my post.
Oh, by the way, I watched other movie from First Look Entertainment
have very good SDH just like Universal Studios did that, but this is bit
smaller font.
I have bad news for whose are loving in near-HD about New Line Cinema is still closed-captioned as mistakenly label "SDH" that I seen "Fat Boy Run", but no SDH on this movie and bonus materials,
but only English and Spanish subtitles. Please note: this movie
with one extra have without closed-captioning but subtitled in English and Spanish is: Thandie's Goof
