Bashō never wrote that haiku.
The haiku is not listed on PoemHunter or in his list of works on Wikipedia, which starts to seem suspicious, but then I found authoritative confirmation at MI6 HQ:
The title of "You Only Live Twice" comes from a haiku (or poem) included in the Ian Fleming novel on which the film is based. It goes: "You only live twice. Once when you are born. And once when you look death in the face." In the novel, the poem is written by James Bond for his friend Tiger Tanaka. Due to a badly-worded attribution at the front of the novel, the poem is sometimes incorrectly believed to have been written by a Japanese poet called Matsuo Basho (See: Bashô Matsuo.) It is clarified in the novel that is should not be considered a haiku at all i.e. it is a poor attempt at writing poetry by Bond after being taught how to do so. The novel and it's epigraph explain that the haiku is "after Basho" i.e. written in the style of the famous 17th Century Japanese poet.
Surprisingly, the haiku has been attributed to Bashō throughout the mainstream media, including The Telegraph and (as you stated in the question) Time, although the phrasing looks so similar that I could imagine one of the articles being 'inspired' by the other.
I'd be interested to know if anyone has a copy of the attribution referenced on MI6 HQ's site to see whether it is ambiguous; unfortunately, I don't have a copy, but I can say with a reasonable amount of confidence that Fleming wrote the haiku and did not intend to attribute it to Bashō.