There is research that asserts the following:
"The Corsair, an air cooled radial engine aircraft, might have been expected to have a higher survivability than the Air Force's liquid cooled (and hence vulnerable) F-51 Mustang. In fact, insufficient oil cooler and engine protection rendered the Corsair just as susceptible as the Mustang to ground fire."
A Revolutionary War: Korea and the Transformation of the Postwar World, Page 138 (Research presented at the Fifteenth Military History Symposium, held at the United States Air force Academy, 14-16 October 1992)
You would need to pull the paper and examine the methodology and data to evaluate the claim. I suspect such a comparison would be a difficult undertaking in the absence of an apples to apples control of relevant variables. I myself would prefer to fight in a Corsair
AFAIK there really is no specific statistical research behind that statement. It really just means that the USN and USMC were disappointed with F4U AA vulnerability in Korea, and the AF was also disappointed with F-51 vulnerability. The USN/USMC didn't publish anything like our favorite 'Naval Aviation Combat Statisitics' for Korea, unfortunately

. No Navy publication or record for Korea AFAIK adds up sorties flown and compares it to losses. My general impression from quotations of loss rates per sortie for sub-periods of the war is that F4U combat loss rates were in the same ballpark as F-51, which were .54% enemy action losses per combat sortie (341 enemy action losses in 62.607 combat sorties), perhaps lower, not a lot lower. Non scientific, and even if we had better stats, unlike the NASC F4U/F6F comparison, the stats wouldn't effectively control for differences in mission profile and tactics, which NASC stats essentially did control for, by quoting rates of a/c *hit* (similar between F4U and F6F) and downed (notably higher for F4U) by AA. In Korea there's no hope of compiling that kind of detail, AFAIK.
The absolute number of F4U's and F-51's lost was similar, 341 enemy action 474 total for F-51's, USN 145 F4U's to enemy action 267 total, Marines lost 164 to enemy action 206 total, not counting 16 AU-1's to enemy action and 21 total. 3 of those F4U's were lost to MiG's along with around 8* F-51's so that was a (n interesting but) statistically negligible aspect of losses. None of either were lost to enemy prop planes against several claims by the US props (it's possible some night disappearances of USMC F4U-5N's might have been to NK night fighters, whose operational details are not known, a couple of Marine F4U/F7F night intruders were jumped by night fighters now known not to have been Soviet or Chinese, in one case an F4U turned the tables and claimed a night kill v Yak-9). Note that the prop loss ballpark .5% per sortie to enemy action, was low by WWII standards; and moreover the focus in both USAF and USN/USMC tended to be high prop fighter losses compared to jet losses, even in ground strike missions. For example, the F-80's enemy action loss rate was only .15%, and Navy jets (and AD's) likewise suffered much less than F4U's.
*per the USAF 1953 Statistical Digest, a not entirely reliable table of losses. An internet urban myth claims it greatly understates air combat losses. That's not true, there are errors but sometimes overstatements too. For example it gives two F-51 losses in air combat in the period before MiG-15's appeared, I identified both mistakes: an Australian Mustang loss included in 5th AF stats, which the USAF somehow thought was air combat but Aussie archives clearly say wasn't, and a typo between 'flak' and 'yak' in the another case, original mission report makes clear the a/c wasn't downed by a Yak). But, the numbers in the Stats Digest are fairly close to what detaile records say, where I've checked, but not always exactly.
Joe