Why do some aircraft have to have the landing gear pinned prior to towing?
The most direct answer is that gear pins are installed to prevent accidental retracting during towing. I'm not typed on the Phenom, but the landing gear actuators are most likely hydraulic. Even if they are electric, the airplane is expected not to have any form of power established during towing, making accidental retraction more possible, even if the gear is held in the down position by locks, not its actuators.

The requirement to install the gear pins is not related to the trailing link design. No matter what the design was, that requirement would be there for each gear.

This requirement is ubiquitous on larger aircraft. During airline operations, I have had an aircraft towed over to me many times. I have never seen a plane in tow, at least at my company, that did not have the gear pins installed during towing.