For that matter, go look up Ivy Bells. Sure, fiber can't be tapped in the same manner, but you can get around that by placing your splice/tap during other outages, especially if you arrange for those too -- "Here's <insert amount> dollars/euros/ducats/doubloons/etc. Drag this across the bottom from point x to point y on your charts on date z, then cut it loose and leave it behind and go on your way."
Now, with a straight face, can you claim that you know, for sure, that your undersea links are pristine and unmolested, either at the end points with the equivalent of the infamous at&t "nsa rooms", or somewhere in the middle? Do you know, for sure, that the people who own the fiber trunks aren't playing ball with the nsa/mi6/dgse/etc?
Unless you own the entire infrastructure, and actively monitor it to be sure of such things, it is best to assume that your communications are vulnerable at some point along the way.