That analogy doesn't work... the Higgs boson can decay, via intermediate steps, into two photons: http://dorigo.wordpress.com/2009/03/04/higgs-decays-to-photon-pairs/
(This is one of the ways it is being detected at the LHC) Thus, in principle it can be created by colliding two photons together, though this is probably a hard thing to do. And photons are massless, hence don't interact with the Higgs field.
This false analogy demonstrates a key fallacy of particle physics - the idea that whatever comes "out" of a collision has to be built from pieces of the particles going "in." Totally false - for example, an electron and positron (aka anti-electron), which are both FUNDAMENTAL particles, can collide, annihilate, and leave only some photons (also FUNDAMENTAL particles) behind. The photons aren't "inside" the electron/positron in any way, but rather, the collision and annihilation of the electron/positron causes a disturbance in the electromagnetic field... which is precisely what a photon is.