Employee refuses to correct her overly confident coworker before she presented her outdated business proposal to the senior leadership: 'She said teammates are supposed to look out for each other.'

She did look out for her in the past, but she didn't appreciate it. 

You can lead a horse to water, but you can't make him drink. This is true across many aspects of professional life. You can tell your friend they need to take their job more seriously if they want to stop getting fired every year, but if they really don't care, you can't force them to. Your boyfriend might tell you that the only way to move up the ranks in your career is to do more networking, but he can't make you attend said networking events: you have to do that yourself. 

It's not always easy to give your coworkers advice if you're on the same level as them. After all, it's pretty gauche to tell your equal what to do in the workplace. Only a manager or a boss should give orders. All that is to say, you can imply and suggest things to your coworker to help them out. If you got in trouble for wearing jeans a couple of months prior and the new hire shows up in jeans, it'd feel wrong not to tell them to avoid doing that in the future so they don't get in trouble. You want to look out for your fellow worker, and unless they are convinced that they're always right, most coworkers will be happy to get advice about things that you've already been through with your company. You're not obliged to tell them, but it's a nice thing to do.