I'm confused here a bit...
I'll have to assume that the light from core is bouncing around inside the sun due to what... gravity? mass? density? It just strikes me as weird that it takes thousands of years for the light to escape.
A key prediction of solar physics, that its nuclear reactions should emit neutrinos with a particular signature, has been confirmed according to scientists at the University of Massachusetts Amherst. Using the Borexino instrument in Italy’s Apennine Mountains, the research team detected electron-flavour neutrinos emitted by …
Got it in three. A photon reacts with all sorts of stuff, notably electrons in atomic orbit, boosting the electron to a higher state, and is re-emitted when the electron reverts to its previous condition. Something like that in the middle of the massively-dense sun can just wreck a photon's speed-of-light plans (and presumably enforce a random walk).
Whether you can call the outgoing photon ``the same'' as the incoming one is an interesting philosophical question. In any case, the energy created at the center of the sun does filter outward excruciatingly slowly, so conceptually it works.
OT: There was an SF novel in the 1960s which opened with a paragraph or two tracing just such a photon over its thousand-year journey, finally escaping the shackles of the mean free path and regaining its birthright at the speed of light. Only to end up irritating our hero by hitting his eyelid the morning after a bender, bringing him unwillingly to consciousness. (Well, I thought it was amusing.)