My reasoning is that neither you nor I work for Apple or Yahoo, and neither of us were involved in developing the Flickr integration for the AppleTV.
Thus, any conclusion either of us come up with is pure conjecture and certainly NOT fact.
. . . ok. But couldn't you say that about any conversation that takes place on Macrumors at all, since most of us don't work for Apple? I don't see how what you're saying is a useful contribution to the discussion. But to each their own.
I'm sorry if anyone here mistook me for an Apple/Flickr/Yahoo employee. I'll happily admit I don't know for sure, just drawing conclusions based on available evidence.
Anyway, back to the topic at hand:
-It is a FACT that Flickr applications on other devices (such as Apple's iPhone, iPad, and iPod Touch, Android, ATT Uverse and even Roku devices) DO let you log in to Flickr and DO let you see private photos.
-It is a FACT that Apple's Flickr functionality on the Apple TV DOES NOT let you do this.
-It is a FACT that Apple designs and builds the functionality on the Apple TV to access third party content (ie: they built the Flickr functionality, the YouTube functionality, the Netflix functionality, etc.).
-It is a FACT that, when asked about how to access Flickr photos on a TV using a particular device, Flickr refers users to the manufacturer of that device (in this case, Apple), see:
http://www.flickr.com/help/account/#1042736
"If you want to view your photos on TV using a method other than AT&T's U-verse, such as Roku, please contact the manufacturer or developer of the device directly."
I look at those facts and draw the conclusion that Flickr would probably happily let Apple build in a login feature on the Apple TV, since they allow it with so many other devices/apps, and I can't think of why they would treat the Apple TV differently. It seems unlikely to me that Flickr is obstructing Apple TV from letting you login. It seems more likely that Apple just hasn't added login functionality because it's not a big priority for them compared to other features they may be planning to add to the ATV.
Admittedly I don't know for sure, but "pure conjecture"? I'd say that's an unfair characterization. More like evidence-based deduction.