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Accessing the iPlayer interface might be by way of some built-in browser, so it may then depend on cookies as to whether iPlayer remembers your HD wish (and would answer why it is independent of the YouView settings).
Don't have a box. Just recently saw some articles about "coming soon" along with alternatives. Must have been on USENET where I saw the links, so will try to find them again.
I got a 30 quid iCan (? will check in next few days, saw it mentioned on HotUKdeals.com a few months back) which is a Freeview HD STB with iPlayer built in. Also had tried the Sony PS3 iPlayer interface. I only mention the browser (above) as I remember one of them giving me a browser error message (I had probably unplugged the ethernet cable, deliberately, to see what happened during "loading" when one had just chosen iPlayer option).
Have a couple of FreeSat HD boxes (no PVR facilities on the ones I chose, Manhattan box from Tesco was 90 quid and got them to install a second satellite dish for upstairs/back of house, to complement Sky dish and Sky HD+ box in lounge). The Manhattan mentions iPlayer etc, but I went into hospital soon after it was installed and have not experimented much with it yet. Also have a Dion Freeview recorder (originally sold only by Tesco) at about 45 quid (via Ebay).
It is a Freeview HD receiver, so gets BBC1HD and other free to air HD channels, subject to your aerial.
I like the search feature, that works quite well and shows when a series is available to watch on demand.
BBCiPlayer module has asked me if I wanted to watch the HD content, even though I had set in the main settings that I wanted HD where possible. Hmm, maybe they need to fix that glitch, may get annoying if iPlayer asks that every time. So far I've only watched one HD thing on iPlayer, so time will tell if it remembers the setting or not.