An overrun is by definition not an "attack action". "When a Vehicle moves through a unit of Soldiers it causes overrun". "Being overrun can cause a unit to be suppressed". The suppression marker(s) are placed as "a Vehicle moves through a unit of Soldiers" as opposed to after the move action is resolved. Combat dice for suppression are rolled as part of the move order during the overrun. At the end of the move order, the unit is suppressed and may not react.
/humorous thought - By whose definition is it not an attack action? Have you ever had to dodge an AFV? Trust me, several tons of steel trying to stomp you into the ground is not exactly a friendly act.
Okay, all kidding aside…
I started my original post to conclude exactly the same point you did. But the more I dug into the rules to prove it, the more I couldn't. What finally convinced me to change my conclusion is if you notice, the rules capitalize game terms. One such term is, "Combat Dice." I believe an Overun is both a Move Action and an Attack Action, because it requires you to roll Combat Dice. Even if that doesn't hold water, based on the wording of Overun and Reactions, I had to conclude you could react at the end of the Overun's Movement. Even if it's only a Move Action, the rules state, "The reacting unit must declare and execute its reaction either before the activating unit moves or after it has completely finished moving." It doesn't say when the Move Action is completed, just the actual movement.
Which led me to point to another example, because it reminded me of the rule where in which a Unit gets suppressed by an Attack Reaction at the end of its Movement Action's movement, prior to its Attack Action during a declared Move/Attack Action in the Unit phase.
Suppression and Reactions rule, Page 47 reads…
"Suppressed units cannot make reactions. If a unit is activated and becomes suppressed by a reaction from an enemy unit, it still completes its activation as normal. Units determine their number of actions at the beginning of the activation (after rolling to remove Suppression markers) and do not, therefore, lose an action if suppressed during their activation."
Since a Reaction is declared at the end of the active units movement during a Move Action, and/or before any Combat Dice are rolled, it must get to react either way, Rules as Written.
I will state however, having dodged a couple of AFVs (one friendly, one not), I hope it gets ruled or erratted the other way (how I first interpreted it, and you play it). The only, "Reactions" IRL to an AFV Overun is to kill it or run before it gets to you, or get squished by doing nothing.