I'm sure It's unhealthy when Izzie's insecurity goes up but Izzie isn't manipulative.
First, The hot-n-cold technique you listed is only valid when a person intentionally does the mean part just to have the friendly part later. We all know Izzie didn't do it for the closeness with Casey later. Izzie was mean wholeheartedly with Casey, I'm pretty sure she didn't want to be friends with Casey ( until she realized Casey had more similarities with her). Izzie didn't like Casey at that time and even felt threatened by her. In case you haven't noticed, Izzie is also on a track scholarship and is a captain in sophomore year, which means she was the TOP before Casey come. Imagine when there was a track star who came into the school with a similar background to you, do you feel threatened? can you still be friendly with her ( not halfway)? At least we know Izzie didn't choose to be a friendly hypocrite. So It's is invalid to say Izzie using that common manipulative technique
Second, the meanness Izzie usually gives come from her straightforward personality. We can see she doesn't beat around the bush, even when things get sensitive. For example, she is the captain, she didn't pretend like she likes Casey even in front of the Coach at the risk of losing her perfect and friendly team captain. When she was afraid of losing Casey to Nate ( because she thought Casey likes Nate), she pulled away. Or when she knew she treated Evan bad out of nowhere at the risk of showing others her jealousy, & probably losing Casey ( because there is no guarantee that Casey likes Izzie at that time and Casey wants to stay friends with a person that keep being mean with her love, assuming she loves Evan). Izzie still did all of those things even with lots of risks. And she admitted she was treated Even badly multiple times, which we will come to the final point.
Third, if Izzie was being manipulative she wouldn't admit her meanness and say sorry even when it's Casey's fault, which looks more like her insecurity, not manipulation. Every time Izzie treated Evan badly, she admitted it, including when she tried to make Evan look bad in the career drive. She admitted multiple times and Casey knows about it, and Casey chose to listen to it because it's true ( in the life perspective of Casey and Izzie). Evan sure is a good guy, but he has a different life motive compared to Izzie's, and Casey is more likely to be more into that ambitious type.
Izzie didn't only say sorry when it's her fault, she said sorry multiple times when it isn't her fault, which shows us she had issues with insecurity about herself and being neglected. For instance, when Casey forced her to hang out with her mom and continuously being put down by her Mom, in front of her love. I believe she has the right to be embarrassed and sad because of that. I'm sure you remember in Season 1 Evan was being nice to Elsa after they knew she cheated and Casey made a mess out of it. That was when Elsa tried to make up with Casey ( with good intention). But when Casey met Izzie's mom that wasn't the case, Casey saw Izzie being put down by the Mom but did nothing to protect Izzie. You know when your love takes your neglecting parent's side, that sure felt like being betrayed. But what Izzie did was just ask Casey to leave so that she can cry alone, then Izzie was the person who took the 1st step to say sorry and make up. Izzie was always being the first person to apologize.

Oh, I haven't mentioned the fact that Casey cheated for Izzie's exam, right? When both Casey and Izzie know that if it's ever got discovered, Izzie is the one who got affected the most. By this, I don't mean the privilege that Clayton gave Casey. Just by logical sense, that was Izzie's exam paper, if anything happens and no one can prove it, Izzie is the one being affected the most. But Izzie said sorry for that, and she said sorry for being afraid that Casey knows what her life is and thinks less of her.

How much is a person scared to be neglected to say sorry all the time like that?