Being nominated is a necessary evil for BB HGs. OK, perhaps in the archives of BB history you may find very, very, VERY rare examples where a HG was never nominated during their season if one even exists (and I'm not counting those who were expelled, i.e. Willie.) But for the most part an overwhelming number of HGs experience nominations. Some sooner than others; some more often than others; and the reasons they are nominated will vary. If you want to say that Kara was a "victim of circumstance" by being on Dan's team, I can accurately state that Shane was ALSO a "victim of circumstance" by being on Willie's team.
How they handle it and what they do to try to survive is mostly on them. They can escape eviction by:
A) Winning POV. By taking matters into their OWN hands and controlling their OWN fate they win POV and take themselves off the block. This is PRECISELY what Shane did successfully and he remains in the House. Kara failed to take control of her fate with this option, so them she needed to go to Plan B.
B) Social Game. Get to know and try to get in good with as many HGs as possible to secure the necessary votes to stay in the game. Kara did not, thus she is accountable for her own eviction.
I agree that losing the first competition put Jodi, Kara, and Danielle is a bad situation due largely to the first stupid twist of the season. But if I'm going to throw even a morsal of credit Production's way, at least they advised ALL the teams what was at stake and the consequences of finishing last BEFORE the competition commenced. With that knowledge in mind they STILL performed miserably and finished last. So Jodi, Kara, and Danielle can all hold themselves accountable.
Sure it would be advisable for Joe, and every HG for that matter, to get to know everyone they're sharing the House with. But you failed to see the key word in my statement--NEED. Joe did not NEED to know everyone in Week One because he was not at risk. Kara, with one foot out the door, did. It was a blunder on her part or for anyone who would be in her similar situation.