They recommend Shinkansen because the "raumen museum" (sic) is a short walk from Shin-Yokohama station.
As I mentioned the bento website mentioned isn't an official website, they don't recommend it because its a short walk, as they say you can get there via regular or shinkansen:
Shin-Yokohama can be reached from central Tokyo in about 45 minutes, or a very comfortable 15 minutes if you splurge and take the bullet train for an extra Y800
Thats whats wrong with the site, in reality its more like 2000+ yen, and what originally brought it up here in the thread.
Of course if you have an expense account its good to take the Shinkansen (man that'd be the life wouldn't it? lol) ..
Stictly timewise speaking, it would depend where in Tokyo you started from, for example if you are staying in Shinjuku, the amount of time to get to ShinYokohama by regular trains would be about the same amount it would by taking a Shinkansen (as you have to make a local connection to Tokyo from Shinjuku then connect to the Shinkansen). About 45-50 minutes in both cases.