In other words, do groups or individuals that launch sophisticated DDOS attacks always do so with a specific motive against the entity (like a grudge) or are people often random victims of the attacker?
Yes they are mostly targeted, reasons can be anything from blackmail, personal/business reasons to just someone who thinks it's funny.
These days any kid with access to a PayPal account or credit card (normally stolen) can cause very big DDOS problems. Due to the nature of DDOS getting enough evidence to target a person or group of people is almost impossible if they are not dumb.
As a side note, it is possible to be the victim of a DDoS attack that is pointed at someone else. It could be another provider in the same data-center, saturating the upstream. It could be the upstream itself is being attacked, or as simple as another site on the same shared hosting server. DDoS while often targeted to do the most damage to one specific entity/group can definitely cause collateral damage.
A lot of times, there is just DDoS flying around, so it never hurts to have a solution in place if a random DDoS outage would have a negative impact on your business.
There are many users of all skills and ages using the internet and this can sometimes lead to unintentional service disruption. It's wise to host with a reputable data center that practices network preparedness for this. With the ever-growing occurance of DDoS attacks, the risk of becoming the victim of random DDoS is increasing.
Consider preventative-maintence as opposed to disaster cleanup.