In the Rohitassa Sutta: To Rohitassa you will find a parallel to this GenjoKoan that you pointed out. For the fish it is the water, and for the bird it is the air. Likewise for the gods / celestial beings, it is the cosmos. This Deva told the Buddha about a desire that he had in a previous life when he was a seer named Rohitassa and its result. He said:
” ‘I will go traveling to the end of the cosmos.’ I—with a one-hundred year life, a one-hundred year span—spent one hundred years traveling—apart from the time spent on eating, drinking, chewing & tasting, urinating & defecating, and sleeping to fight off weariness—but without reaching the end of the cosmos I died along the way. So … ‘I tell you, friend, that it isn’t possible by traveling to know or see or reach a far end of the cosmos where one doesn’t take birth, age, die, pass away, or reappear.’”
In the above Sutta, the Buddha says that the end of the world cannot be reached by going the distance. Buddha said that only by finding your own self, or in other words, it is the understanding of oneself as one really is, that one would see the light. As the Rohitassa Sutta states, these truths are concerned with the "one-fathom long body of man." The key-note of Buddhism is this right understanding.
To get to know what life is, one has to first come to Samma Ditthi. Samma Ditthi is in short, Right understanding. Right understanding is explained as the knowledge of the four noble truths. In other words, it is the understanding of oneself as one really is. One pre-requisite of one coming to ‘Right View’ (Samma Ditti) is learning to welcome advice of the Supreme Buddha with delight. We must not treat even a single verse of Dhamma as being plain and simple. We must learn to treat the Noble Dhamma as supreme. We must consider this Dhamma to be the most profound.
It is said in the scriptures… “ Pemato jayati soko, pemato jayati bhayam”. [From affection springs grief, from affection springs fear]. Conventional minds will recoil to the idea. But it is seeing this other side to life will one get to know what life is. The truth and meaning of Dhamma becomes a private experience by the wise only when there is insight or vipassana. But vipassana depends on samadhi or concentration. And samadhi depends on Samma-ditthi. Thus, everything in Dhamma is connected. Why is that? The Buddha is speaking, albeit in diverse ways, only of one thing and one thing alone – dukkha and the cessation of dukkha.
This Noble Dhamma is Svākkhāto (it is well proclaimed). Nothing needs to be corrected in this Dhamma (found it the Sutta & Vinaya – the first two baskets) and nothing can be discarded on the basis that it is too plain and simple (if one understands this quality, then this person comes to Samma Ditti— right view). This is why we must hold dear the advice we receive and use that noble advice to discipline ourselves than vice-a-versa.