I don't think that's correct. Recall will not draw any data from any app you don't actively display onscreen. In fact it will not draw any data you don't specifically display on screen. Apple's Recall will know about data that is stored in applications whether you open it or not, as it's been explained, but it will work with specific applications drawing from specific data (and it does also look at your screen, although it's not clear if it does that constantly or on demand).

Just to quote the current Apple Intelligence landing page. This is posted by Apple itself as promo materials:

Apple Intelligence empowers Siri with onscreen awareness, so it can understand and take action with things on your screen. If a friend texts you their new address, you can say “Add this address to their contact card,” and Siri will take care of it.

Awareness of your personal context enables Siri to help you in ways that are unique to you. Can’t remember if a friend shared that recipe with you in a note, a text, or an email? Need your passport number while booking a flight? Siri can use its knowledge of the information on your device to help find what you’re looking for, without compromising your privacy.

Seamlessly take action in and across apps with Siri. You can make a request like “Send the email I drafted to April and Lilly” and Siri knows which email you’re referencing and which app it’s in. And Siri can take actions across apps, so after you ask Siri to enhance a photo for you by saying “Make this photo pop,” you can ask Siri to drop it in a specific note in the Notes app — without lifting a finger.

That sure sounds to me like Siri now looks at you screen, logs your past activity, or at least searches through pre-existing system logs of your activity, and has access to and processes all your information.

Again, Recall and "AppleI" will both draw different sets of data, but they are both drawing new data at the system level. And they're both making context inferences on your data. Sure, the process is different, they each have issues the other doesn't (MS's 1.0 version had glaring security holes and it's too human-readable, Apple's version is sending your data to a server for processing, instead of being all on-device), but it's fundamentally doing the same thing with the same startling access to your data. Both companies insist they're not logging your data anywhere outside your device. To me, that's not enough in either case.