That wouldn't be entirely fair. Quite a lot of attacks come via compromised kit that can't be fixed because a fix hasn't been released yet.
The angle I typically work is to hard block the offending IP range, which usually triggers a complaint by a client or a customer, which gets fired up the chain and grabs attention of someone higher up who usually has the clout / contact details to get in touch with someone else higher up in the offending company.
Personally, I'm never quick to judge another sysadmin...just because an attack appears to have originated on their network, doesn't mean actually did. Where possible, I'll contact a sysadmin directly, introducing myself as another "fucking knackered" sysadmin (which usually creates a level of rappor and understanding from the get go) and I'll work with them. I will never fire off a snotty email to a sysadmin telling them to "sort their shit out" or anything like that. We're all buddies here, alright?
For example, I run a mailing list server for a client and in the past (when I inherited the system and before I was able to lock it down), at the time it was the wild west, anyone could send an email to the mailing lists and it would just bounce through...naturally, as you've already suspected, this was a massive problem when it came to spam. Someones sysadmin came down on me like a ton of bricks, because when the email passed through the mailing lists, it was re-sent using a mailing list address, the sysadmin, like the tosser he was, just went for the throat...anyway, some of his people started getting an avalanche of crap and he pointed the finger at me...which is fair to a point, but I was hamstrung at that point so I couldn't lock down the lists, but I couldn't stop the spam either because it was originating outside of my network of users. Anyway, long story short...the origin of the spam (thanks to some email header sleuthing) turned out to be a machine on his network. I was polite about it, and he did wind his neck in...but man he was sheepish in follow up phone calls and he got a scathing public bollocking on a conference call from his boss with us.
Remember kids, don't be a dick to other sysadmins, if you're nice...there is a good chance that a fellow sysadmin might help you get a problem resolved and keep it off the radar...helping you to avoid looking like a dick and avoid getting your ears chewed off by your boss.
Most importantly, if you treat other sysadmins with respect, you now have more than one person helping to resolve a problem...you're not alone stressing the fuck out...you may also benefit from some "back channel" knowledge sharing that you can't get anywhere else. I've shared and received valuable advice and tips with sysadmins steadying other ships...I don't know them personally, I may never speak to them again...one of them might be you in passing in the future...but I've probably learned more useful stuff this way than any other way. Little golden nuggets like Powershell hacks I might no have known, hidden registry keys that are worth knowing, config tweaks to improve performance / security...you name it.
Sharing is caring. Be excellent to each other.
...and fellow sysadmins...I'll see you out there!