Is there a way to tell if paid ads are just taking credit for installs that would've happened anyway?

Yes, with a holdout test. Attribution shows which campaign touched a user before converting, not whether it caused the conversion, and retargeting and brand search are where that gap tends to be widest. A holdout keeps a random set of users, devices or regions from seeing the campaign and compares the results: if the exposed group converts at 5% and the holdout at 4%, the campaign added one point, not five. Common splits hold out 5% to 20% of the audience. Pick one metric before you start, randomise properly, keep held-out users clear of the same message on other channels, compare total conversions including organic, and run for at least one full purchase or usage cycle. For channels you cannot target by user, use a geo holdout; Meta and Google also offer lift studies. Run these a few times a year on your biggest budgets. Background: https://linkrunner.io/glossary/what-is-incrementality-testing