I have (grudgingly) admin'ed such a server, and will readily admit it as a form of public shaming (though not of myself, as you'll soon learn).
As TFS points out, the attackers didn't use a zero-day exploit. They didn't use an unpatched old exploit. They didn't even use the fact that huge "trusted" swaths of the filesystem, including standard executable paths (such as /usr/local/bin) had both the directory and everything contained within world-writable (no, I didn't have the option of fixing that - it would have broken "features" of the reason this box existed, as I'll soon explain).
This system ran a fairly popular POS software suite, and absolutely depended on all its serious security flaws. The vendor had even installed what amount to pre-compromised binaries for "convenience" in diagnosing end-user problems (connect to the right port, bam, you can monitor any user's session). But even that egregious level of incompetence didn't cause the breach.
No, the breach came from the fact that the vendor had their own company name as the root password (and had it hard-coded in literally dozens of (world-readable) scripts, so I couldn't just change it). And did I mention, the vendor required this box have a publicly facing IP or they'd refuse to honor their SLA?
Needless to say, my first action on learning all this, I blocked it at the firewall and told the vendor that we'd let them in when, and only when, we needed assistance. That, amazingly, enough kept the box safe for about a year (and floored me that we hadn't gone down long before I got stuck with that albatross)...
Until an upgrade. Took a total of half an hour. Didn't matter, because we had someone in as root in a tenth that time.
But, distant past. Couldn't happen again, and no other vendor would ever have such an extreme level of cluelessness, right?
So, currently, I work with (but thank Zeus, don't have to administer) a CRM system by an entirely different vendor, running on an outdated Linux distro. Pretty much everything I just said applies to this box. But hey the firewall keeps it safe, except the once-a-year the vendor demands access to audit our license compliance...
So yeah, Linux systems get hacked - For reasons that wouldn't protect the otherwise-most-secure system on the planet. You want to make it stop? Tell your vendors to go fuck themselves when they rationalize having a weak root password, and piss-poor system-wide security, and ban patching known vulnerabilities because it "might" break something the vendor used. Really that simple.