It's definitely possible and it's happened to me more than I'd like to admit. I feel a lot of it stems from folks not stepping in and admitting theirs or others' faults.
I did a second tour a baml and did some of their release management. We hired a new guy who was technical and smart, but never listened to training since he was busy texting all the time. So, when he typo'd and all builds started failing, the fault was put on my shoulders and didn't want to admit fault. My manager wouldn't listen to what actually happened. I think I was out of there maybe two months later after they chose not to renew my contract (which thankfully force broke some golden cuffs). The guy who messed up is still there, I think. tl;dr baml sucks.
Another time at a medium sized company, there was a new ~really cool~ NOC being built that everyone wanted to check out. My boss took everyone up, but a locked door was in the way and I was given permission to open it with a CC. A week later, two other guys on the team did the same thing, got caught by security, and almost got fired by the CTO directly. My boss, at no point, stepped up and admitted he did the same. When talks of firing started, I made it very, very clear to him that if those two got fired, I'd make sure that both of us would be fired, too. Nobody was fired, so it might have actually worked, but it's incredibly shameful that of five others involve, nobody stepped in to add correction.
That same place also created artificial competition by only having one fulltime opening for the 6 contractors. Lots and lots of subtle backstabbing as a result. When they gave me the position over the other guys who'd been there for a lot longer, things became very oddly hostile.
I have more stories like this, and yes, it happens at big, large and medium companies, but it's so much easier to do it at bigger companies.