KVM P-I-P... Privacy Issues With Remote Connections

Question... my firm is investing in a KVM switch that supports P-I-P technology so that we can simultaneously utilize and view four separate computer systems.

Computer 1 is the "main" system that controls many of our assets. The other three are slightly less utilized but contain sensitive information that is often left on screen for trouble shooting purposes.

Computer 1 is often connected to remotely by staff members for a variety of reasons.

Here is my question... if Computer 1, Computer 2, Computer 3, and Computer 4 are all going through the KVM switch and the feeds are being split onto a single monitor, is there any way that someone remotely accessing Computer 1 could see the screens on the other three systems? (Would they even know a KVM switch was plugged in?)

Thank you.