Must? No, you can change the ISO. Like all triangles, the exposure triangle has three sides.
It's been a few months since I
posted a couple of good links that explain equivalence. I'm guessing you didn't read them, but I'll post them again in case someone other than you actually wants to try to properly understand the concept.
This link has a thorough explanation of the concept:
This link is a decent summary:
Equivalence, at its most simple, is a way of comparing different formats (sensor sizes) on a common basis. Sounds straightforward enough, but the concept is still somewhat controversial and not always clearly understood. We thought it was about time we explained - and demonstrated - what...
www.dpreview.com