Around 2005, Intel was shipping hot-running Netburst CPUs (Prescott and Pentium D) with rather high power consumption. These would have strained capacitors and contributed to premature death because heat is very, very bad for electrolytic caps--and no one was using solid caps back then due to price.
This period coincided with intense competition between motherboard manufacturers, and there are a lot of brands from that time which no longer exist. Seriously, half of the mainboard manufacturers went bankrupt or merged, including my two favorites. Capacitors are a frequent target for cost-cutting. Cheap caps are a terrible idea in anything that is intended to run for years. But, hey, market pressure.
So caps fail with time, and they always will. But, yeah, there was a perfect storm in the early-mid 2000s that caused an epidemic.
Also true. Those two CPU lines put strain on mainboards and heated up cases hot. Of course, around 2007, you're most likely talking early Core 2, which were far cooler. The "Press-hots" were more around 04-05. I remember getting a lot of Dell Optiplex GX270 mainboards replaced due to heat issues with the Prescotts and mediocre capacitors causing a perfect storm of problems - the desktop case models were horribly problematic (not enough ventilation space).
Nippon Chemicon is usually a good capacitor. However, another key feature is what the mainboard manufacturer spec-ed. Expected operating temperature plays a difference, and if the vendor cheaped out with caps not rated for either the demand, or as good of a temperature rating as needed, and this could happen.
I'm going to make a guess; a scientific wild-ass guess, but a guess still. The right picture has silk-screening that ends in AM2, which could mean a Socket AM2 board (Athlon 64, Athlon 64X2). The budget AM2 boards I know of from that time (Foxconn made ones in red, I remember those, and a few others like MSI did as well on the lower end) had less expensive caps, and this wouldn't surprise me at all. And Ludi is totally correct in that that's probably one of the warmer areas of the system board too.
One final thing: While less likely, Nippon Chemicon capacitors have been counterfeited, just like ASUS mainboards and Cisco networking gear has. If not sourced direct...*shrug*