I'm going to chalk this one up to a Bethesda issue.
Those of us have played the game know that there are people who are synths that, when they die, don't drop a synth chip. I would literally need to rewrite a LOT of my story based upon something I just found out today. Apparently Sturges is a synth. At least people who have made him a non-essential character (since otherwise you CAN'T kill him) have done so, and he drops a synth chip. Since I've never seen it when I've tried to pickpocket things from him, and you DO see it on some other people that you KNOW are synths - and some who ARE synths don't drop them when they die, I'm going with the "he's not a synth" at all.
That's my story and I'm sticking to it. Just consider it a 'mod' that I've done, in case you were also like me. Mind you, I've only played completely through the game something like 20 times, I have it modded heavily on my Xbox One, and I use the wiki for a lot of things ... and this is THE first time I ever saw that about Sturges, years after the game came out.
Other than that, hope everyone is still liking what I'm writing!