It's called Jackson Hole BS/marketing hype. That number is from the summit Tram and does not relate well to the rest of the mountain. Even their Mid-Mountain is at the summit of Bridger Gondola about 2/3 the way up.
The "marketing hype" number is from just above the top of the Bridger gondola. Measurements were first taken there in 1998, the year after Bridger gondola was built. The mid-mountain site really is at mid-mountain elevation 8,180 and dates back to at least 1968. But if you look at actual ski terrain there is probably 3x as much below 8,180 as above (Hobacks, Apres Vous, etc.).
There are 4 measuring sites at Jackson and you can look up their history
here. Organization is not by site but by month. Put in a month and you get all 4 sites for that month going back to 1974-75. Data is complete Nov.-Apr. since 1998-99.
The base at 6,510 feet averages 141.78 inches
Mid-mountain 8,180 feet averages 364.66 inches, essentially the same as the 369 I use for that site since 1971.
Raymer 9,360 feet is the site above the Bridger gondola and averages 456.49 inches
There is a site in Rendezvous Bowl 9,580 which averages 433.07 inches but it is more wind exposed and erratic.
Ironically, Jackson's record snowfall season mid-mountain was 572 inches in 1996-97, the year before Raymer opened. Raymer has exceeded that number only in 2008 but was probably over 700 inches in 1996-97.
Season-to-date numbers on Jackson's website are also since Oct. 1 and and the Raymer number is what's always in that graph and any press releases. But I give JHMR management credit. At least they publish the numbers by Oct. 31 and also include the mid-mountain so I can use a Nov. 1 start at mid-mountain for realistic comparisons to other ski areas.
By contrast Park City only publishes top of Jupiter Bowl in-season so I use 80% of that and get the more representative numbers from Summit House at the end of the season. I also don't get mid-mountain Alyeska until end of the season. Alyeska currently reports 207 inches snowfall at top of lift service, but it also reports being 30% open on a 18-68 inch base, which tells me there has been a lot of rain lower down.
I still believe it would be unwise for sbooker and family to go to Jackson this week. The lift system there does not handle crowds well and I think they will find the powder less competitive and more in their comfort zone at Targhee. And how fast Jackson gets more than 50% open with ongoing storms and extensive control work remains to be seen (this applies to AltaBird too). ChrisC is right about the goggles at "Grand Foghee."