Kill steal, or kill secured?

So, I just played a blind pick game as Syndra in mid. She's becoming my main, and I've literally been playing her non stop, and I usually dominate mid, and the rest of the map once I snowball off a few kills there and when I roam bot to help. This isn't really about how to play as her, but rather this whole concept of "you stole my kill, bruh ;-;" mentality.

Now, I'm new and just started playing in like Februrary 2015. But I'm under the impression that the support isn't supposed to get kills and is supposed to set up the adc to finish and take them. I get that. Feed your adc and you'll more than likely win. However, here's the match-up for that round; champions listed first were on my team:

Top lane: Darius vs Nasus Mid Lane: Syndra vs Lux Bot Lane: Vayne and Volibear vs Jinx and Vel'Koz Jungle: Fiddlesticks vs Tryndamere

About ten minutes in the game, I'd killed lux twice and was level 10-ish, and Darius asked for help. I went up, and then Nasus went MIA. Darius pinged to the bushes and he face checked them. Nasus engaged, so I jumped in. Then Nasus obliterated him before I could even q, so I did my q-w-e combo and killed him.

Shortly after, Fid was trying to steal their blue. Lux and Nasus were both there, and they started fighting. I went up to help, and landed a q. I w'd to stun, and it consequently killed both of them. I was now 5-0. We were all at about half HP. I headed back behind baron to back, but then tryn popped up and killed fid. I came about and Darius engaged, then tryn nearly killed him. I q'd and ulted, and killed tryn as Darius ran away. 6-0.

Both fid and Tryn started complaining saying I stole both of those kills. Fid claimed he could have had a triple. Darius said he would have at least have had a double.

When Jinx and Vel came up right after that fight, I quickly eliminated them. Bot lane didn't complain because they were losing lane hardcore, anyway. But Fid and Darius kept whining about kill stealing.

So guys, what do you think? I believe in kill secured with random situations where there is an actual kill steal. (For example, I'm soloing a lane, laying into my opponent and they have like 10 hp left, then the jg just rolls in, autos and takes it... I'd consider that ks). But especially in blind pick normals, I think that in a team fight, if we get out with less casualties than the other team, we're better off. I've got my priority targets, and I'll do what I can to kill them. If someone else gets it, then it's whatever.

I get the frustration of Fid being 2-14-11 at the end of that game, but it's team game. What do you guys think? Is kill stealing a thing in team fights?

By the way, we lost that game because I'm not good enough to carry lol.

My team:

Vayne: 3-19-5 Volibear: 4-5-9 Syndra: 14-3-4 Fiddlesticks: 2-14-11 Darius: 5-5-9