I'm one of those shooters that take a very small number of select shots per day which justifies the permanent use of raw files. I'm content to leave the thorough snap snapping to my friends. However I do realise that many here do prefer the latter style, and unprocessed jpegs are desirable to them, and if the camera has it, why not?
Therefore the claim by panasonic that their gx1 will have superlative jpegs (paraphrased) is of considerable importance to many.
My point of view is that Jpegs have the same potential, as long as the camera allows you to adjust the settings. I've owned or had extended access to 3 olympus cameras and 3 panasonic cameras, e-pl2, xz-1 and e-p3 borrowed, gf2, lx5, and gf3 borrowed. I've never been happy or unhappy about the quality of the OOC jpegs that I've seen, but I've seen some proclaim that olympus' jpeg engine is a significant reason to consider an olympus over a panasonic.
Looking at the panasonic's second newest jpeg engine compared to the olympus one it seems like panasonic has lifted their game up enough for 'olympus jpegs' to not matter, but the bandwagon is still rolling.
Pretty much factory settings, both jpeg, +1 sharpness, +1 contrast, 0 saturation
Panasonic profile: Standard
Olympus profile: Natural
Auto WB, panasonic

Auto WB, olympus
The olympus is very warm. If x is the ideal, both are quite close but the tint is just too strong.
colder----px--o--warmer
Card set WB, panasonic

Card set WB, olympus
The olympus has a strong magenta/red tinge, reminding me of velvia, while the panasonic is far more accurate.
Though I have not tested, I would subjectively say that the ooc jpegs from my e-pl2 are more pleasing than those from the lx5, but it is likely that I was under the placebo effect, as well as expectation bias.
Since both are without WB micro-adjustments, it would take a couple of button presses on both ends to obtain whatever result you'd want, whether accurate, warm, or cool. The abundance of profile and micro-adjustment settings offers an enormous pool of possible combinations to achieve the look that you want. This suggests that people have been basing their observations on old jpegs, jpegs that have been produced by suboptimal user settings or are just biased by the placebo and halo effects.
Considering the adaptability of any camera's jpeg output and the performance of panasonic's latest processor, I would expect that panasonic's claim is realistic in the subjective sense, but objectively minor.
Note that AB comparisons in photography are solely for philosophical purposes, as if you subjectively find A adequate, nothing else matters.