They know how to run them in that they have web services running, but I'd contend that they're not run very well. They are consistently slow, slow, slow, not to mention buggy.
I just opened the Mac app store application, clicked the "updates" tab/button, and waited 15 seconds to be told that there are no updates available.
When I install app updates on my iPhone (5, running iOS 6), the badge icon does not go away until I re-open the app store app, on a consistent basis (greater than 50% of the time). When the badge icon does show updates, tapping the updates tab produces a wait similar in magnitude to the Mac app store example above, even though the app already knows there are updates available, since it showed me via the badge icon!
Apple's web services, in my experience, are comparatively slow when viewed alongside other major providers of web services.
On the "slow, slow, slow" point, I didn't realize how slow iTunes was until just now.
I recently got a couple of HD movies for my Nexus 7 from Google. I didn't really think that much about downloading them, just stuck the pin and they were downloaded reasonably quickly and painlessly in the background.
But now that I think about it, the contrast with my wife's experience downloading HD TV shows and movies from iTunes could not be more stark. The downloads take hours. She'll often check and be frustrated about how little had downloaded. She'd sometimes end up reshuffling her downloads. Until our recent wireless upgrade, she'd worry about where to place her laptop, sometimes resorting to a network cable. And probably more frustrations I'm forgetting.
To top it off, this is in a country Apple officially supports and Google doesn't. From my (admittedly limited, external perspective) I'd say Apple still has a long way to go with web services, including iTunes.