I thought it was a trick question related to the fact that a lot of well known airports associated with cities are not actually in the city limits. For example, Sacramento International Airport is not in Sacramento, so you can’t “fly into” Sacramento.
I call foul. Many worse misspellings pass scrutiny here. And don’t any state capitol structures support helicopter pads? I’ve taken commercial choppers around Los Angeles. A chopper pad atop a state capitol would facilitate quick escapes from angry mobs.
My trick question has an easy answer: Dover DE, because no commercial flights infest the state of Delaware. At least Salem has in-state access. If you can’t fly commercial into a state, its capital city is stranded like an abalone at high tide.
Been there, done that. For 49 of them, anyway. While we’ve been to Alaska we were not in Juneau.
Collected state capitol police/state police patches at every capitol we’ve been to.
Whether the nearest airport is in the same state or not should be irrelevant. You certainly didn’t put it in the question. At any rate, Googling gives three different answers to the road distance between Dover and Philly International and they fall into the range of 66 to 71 miles. The distance from Topeka to KC International is 72 miles. So if you can’t fly commercially to Dover, you can’t do it to Topeka either.
Sort of an oops. I found out that Mahattan Regional Airport does have commercial flights. It’s slightly closer to Topeka than KC Int’l. and about the same (69 miles) as Dover to Philly Int’l. That doesn’t change my point, though. If one is served by commercial flight, the other is too.
pkbites:
Ditto for me and my wife, but we did it in five years rather than 20. But we didn’t count a state unless we’d actually done something (at least one thing) there, not just pass through. We’ve also re-visited states multiple times.
[Moderating]
Since this thread seems to be almost entirely personal experiences and discussion of “what counts”, it’d probably fare better in IMHO than GQ. Moving.
I think the answer to . the OP gets into how you define “visit”; I like the one your coworker used. I know people who have done most, or all, 48 in 15-20 days or there-abouts but most states were drive through and some like WV were driving through the thinnest spots possible. That isn’t what I personally would consider a visit. 
On a fund-raiser, two of us drove through 21 states in 52 hours. Speed limit was 55 then. Packed food, so only cost was gas. Stopped in each to make a collect call back, to prove we were there, which took two hours time…
My GF once got one of those national parks passports, and we stamped it in 48 states in a year, and I had a part-time job to go to every week. So you can really do them as quickly as you want – just do it, according to your own definitions.
I’ve been to every state except North Dakota at least twice, with the visits separated by at least a year. (I expect this year to catch ND for the second time.)
I think I lack just 3 states on my “piloted a small plane over” list.
Working hard on my “visited all US National Parks” merit badge - about 5 left to go. (It’s something of a moving target - more are added from time to time.)
Pearls Before Swine has a tip for visiting all 50 states.