Sony's online infrastructure is actually fairly good unlike Nintendo's, though. Plus, unlike some here seem to believe, I don't think they will rewrite a significant portion of Splatoon 2's code to change the online to servers (not to mention servers also have problems), so... Not much will change. Oh well, $20 is definitely not that expensive.
Knowing Nintendo, when they announced paid online, I expected $50/month or something.
Sony's (and Microsoft's) pricing is just obscene by the time they keep raising it. I stopped paying after the last rate hike. The price is all about subsidizing other people's free games. I don't download them, so it's just me buying games for other people. Blech. Sony's online....I don't know, their PSN download speeds are pretty abysmal. I haven't really played much online on Sony, so I don't know how their online works, but last I checked it's the same P2P that Splatoon is at least for Sony 1st party games.....so same service for triple the price, and arguably worse downloads... I haven't dealt with XBox in a while, but I do recall them having decent online.
I'm skeptical about the dedicated servers as well though. The rumor was from a credible source, but yet it doesn't make any sense to me that they'd go through the expense of running dedicated servers. I'm assuming it won't happen, but if they did, not only would Splatoon be a LOT better, but it would be amusing to see them trounce Sony/MS at their own game for a fraction of the price.... And I also can't imagine what's causing the endless delays in the paid service unless they were adding a lot of infrastructure. It would be a shock move, but the concept isn't baseless.
As for Splatoon, I can't imagine they'd need to rewrite anything. More to the point, any netcode required to support client-server versus P2P would probably already be in the executable considering the dedicated servers (if they were ever actually planned) were supposed to be up and running by the time the game initially went gold, not 6 months later. Best I can tell, the game clusters the lobby into 4 client-server pairs (thus one DC often takes another down with them and full DC usually leaves you with one other "player".) I'm not sure how it coordinates the 4 mini-servers, whether one acts as the coordination server, or they all just sync, or if some of that's on Nintendo's end already to coordinate them. With LAN play already present in Splatoon 2, the netcode underneath is already very different from S1...even if right now they're falling back on the old design.
TL;DR; Yeah you're probably right, they're probably not doing dedicated servers :P But the possibility does exist.