While copper will work harden, it only will under conditions where it is allowed to flex. A properly fastened and isolated copper line shouldn't be a problem and since the OP is asking about providing a bead so that the rubber hose cannot slip off, he is providing isolation from the work hardening vibration by virtue of the rubber hose. A stainless line is subject to work hardening as well and depending on the grade of stainless, maybe more so than copper. The mention of stainless lines in factory applications is referring to a formed, anchored line.
The corrugated, bendable stainless that was mentioned is designed and specified for a solar application, and would never see any vibration as such. In this application, work hardening is not a concern. What would be a concern is making reliable connections to the corrugated pipe. I may be wrong, but I think this pipe is similar to a product we use in gas fitting called Trac Pipe. It is a corrugated, or more correctly, convoluted plastic coated pipe designed for gas applications and as such, has specially designed termination fittings that allow for a leak proof seal between the convoluted pipe and other connections.
For a 3 foot piece of pipe, properly attached to the vehicle chassis and isolated by rubber ******* at the terminations, a piece of plain old copper tubing will do just fine.
And Matt, it would be interesting to hear you explain how the pressure in an automotive cooling system, which is regulated by a pressure relief device, either on the radiator cap itself or on the coolant tank, can get to 75 PSI. Thermostat open or closed.