Unfortunately it's one of those situations were you can't afford to ignore the political side of it, specifically the socio-political aspect. The "Thank you for your service" thing strikes me as being totally socio-political in nature as we have seen the governments and media encouraging citizens to say it. More so because it helps pacify any potential dissent about whatever war we might be in at the moment than for any true care from the government or media about service personnel. It didn't spring into life from the community as a way to show gratitude, it was very much an orchestrated event.
But this is also the part that really illustrates the divide between former & serving military and civilians. With the "Thank you..." being repeated so often by politicians and media talking heads and others who have rarely (if ever) set foot near a military base, it starts to feel like nothing more than an empty platitude.
I can very much understand any military personnel taking "Thank you for your service" as really meaning "Thanks for doing the shitty things I don't want to do".
On the very few times it's been said to me I found myself doubting the sincerity of the speaker because it very much seemed that they were saying it because they seemed to feel it was expected of them - they didn't really appear to care about whatever I might have done during my time in, but they felt they should say something because it's the politically correct thing to do at the moment.
And here's you doubting my cynicism