While that may sound like a simple solution, it's waaaay more complicated than that. The app doesn't appear to have any account authentication at all, so that would have to be implemented. Then, they would have to figure out a way to link the calendar data on the website with the calendar data on the app. THEN, they would have to figure out a secure way to link the account on the app with the account on the website. Only then would they be able to go through the process of figuring out how to sync the user account data between the two.

So, yes, ideally, that is the solution, and even more ideally, the entire calendar system would have been designed like that from the get-go. It's much easier to design a system like that from the ground up than it is to try to shoehorn two completely independent systems together. It would probably take a small development team several weeks to do all this, assuming the app was even capable of that level of customization in the first place.