I believe that a persona could perform the invite mark action, but not a device. Puppeteer could be used to force a persona to make the Invite Mark action, but this does not answer MY QUESTION. Can my smartgun make the Invite Mark matrix action? Or any other device for that matter?
Please consider my thread question "[SR5] Can a device perform the matrix action Invite Marks?" because it DOES NOT mention puppeteer.
From a purely "technological" standpoint: yes, clearly any Matrix-connected device is capable of inviting a persona to mark it, just as any current-day smartphone is capable of placing a phone call to 1-900-MIXALOT. Can they take the Invite Mark action? Not by RAW, despite there being numerous references to devices/hosts/icons inviting marks without an Owner taking the Invite Mark action.
Now, going to your specific example of the street samurai somehow derping it up and trying to use the Control Device action to tell his goggles to Invite Mark (rather than just taking the Invite Mark action himself): I think that you're over-complicating the issue and letting game terms get in the way of the "reality" of the Sixth World. If an Owner wants something that he owns to invite a persona to mark it, then the Owner is taking the Invite Mark action whether he knows it or not. Even if he's somehow connecting through some weird remote-control via his commlink or whatever, it still boils down to an Owner telling a device to Invite Marks. (That's my interpretation, anyways).
Now, with all that said, let's get back to the concept of icons taking the Invite Mark action independently of a specific command from their owner (such as the 50000 marks issued daily by the Seattle Public Library system). I can only think of a few circumstances when this might happen, with varying mechanical support for how they would actually work in-game:
1) Puppeteer: perhaps the gold standard of "can this Invite Mark or not debates. Strictly by RAW it doesn't work, though I personally would argue that it *should*.
2) Spoof Command: under the most stringent of interpretations of RAW it might not be kosher, but it certainly appears that it should work (since you are ultimately pretending to be the Owner of the device)
3) Some manner of automation (such as your IC/Agent examples): nothing concrete from a rules mechanic sense, though the argument could be made that Agents (who can "perform Matrix Actions for you") could do it.
4) Some manner of blanket Invite Mark command issued by the Owner ("Invite the next 25 Emerald City Grid users who come by to mark you for 30 minutes"): I think that it's a stretch, but the argument could be made that it falls under the Invite Mark action. Probably the "cleanest" way to assume that the mass Invites that the fluff seems to indicate occur actually work under the RAW.
5) Some manner of device malfunction: if the GM wants to say that some device or another just invites a persona to mark it for some technomalogical reason or another, then it does. Strictly handwavium of the highest order.