In this graph, you have clearly found the triangle composed of three curves which is the smallest one. The triangle made of $gg$, $ZZ$, $\tau\tau$ near $m_H=130$ GeV is comparably small but larger.
Still, none of the triangles is infinitesimal. Even though your triangle is the winner among the small ones, it doesn't show an intersection of three lines. So it's not exact. This property of "three lines intersecting at a single point" is fully analogous to the discussion of "gauge coupling unification". In the Standard Model, it's not exact although the triangle is similarly small and thin, just like yours.
In the MSSM, one modifies the spectrum so that the intersection of three lines, depicting the gauge couplings for $U(1)$, $SU(2)$, and $SU(3)$, is exact within the error margins. It also has a good reason: the groups become subgroups of a larger unified group such as $SU(5)$ which only has one coupling so the smaller groups' couplings have to agree at the GUT scale. In your case, no such improvement is known. At any rate, your lucky hunch is a coincidence, the triangle is not "anomalously small". Its size is not far from what you expect from the smallest triangle in a similarly large chaotic graph with intersecting curves.
So it's a coincidence. If you wanted to use this "near perfect intersection" to argue that 115 GeV is special, the LHC has proved that your intuition was wrong because the Higgs mass is known to be 125 GeV today.