I do not work on X, but I am being asked, because if I do know the answer, my team leader knows I will give the honest answer (rather than telling them what they want to hear).
You should continue to tell them honestly that you do not know, then. It sounds like your team leader has a great attitude about this, but might be relying on you too heavily for things that are not your responsibility.
If you are looking to move up the chain, or get a raise, etc. then it's good to look for ways to improve your reliability and increase your responsibilities, but keeping tabs on your coworkers's tasks isn't that. Managers and their reports should be responsible for appropriately communicating between them how projects are moving along and the like. There's nothing wrong with your boss getting a secretary to help manage information and their schedule if they needs one, or splitting the team and hiring/promoting team leads below him, but it is not your job to track this information on your peers unless you/they are aiming to take on that kind of job. (You should, of course, have a good idea of the status of both solo and collaborative projects that you are actively a part of.)
It is odd that you are leading the team standup while the team leader is either absent or not paying attention. This is their job. Are you sure you are not beginning to manage the team? Does your team leader manage multiple teams? There may need to be a change to the process or reporting structure here.
Do take notes if they would be useful to you for your own purposes and those of your role. Stand-ups are meant to be an effective tool, don't let philosophical arguments prevent you from making them more effective for you. Don't, however, take notes in order to bridge a gap that has nothing to do with you.