The center of the Sun is extremely dense, and a photon can only travel a tiny distance before running into another hydrogen nucleus. It gets absorbed by that nucleus and the re-emitted in a random direction. If that direction is back towards the center of the Sun, the photon has lost ground!
It's not really the same photon, though, is it? It's just some measure of energy.
What do you think a photon is but a measure of energy?
Imagine you shoot a puff of air across a room (presumably using an Air-zooka(R)) and score a direct hit on me. If I turn around and say, "I can't believe that puff made it all the way across the room," you could object to my comment by saying "It's not really the same puff of air; most or all of the molecules in the original puff are still over here." But this just obscures the fact that a puff of air, as people use the term, really refers to the wave pattern of cause and effect that travelled across the room. The gas molecules that are inside such a puff at any given moment are incidental and ultimately not what I'm talking about.
Indeed. But it can be hard to do any kind of science popularization if you don't allow yourself to talk about time in a non-relativistic way (when it's not germane to the main point). We just don't have the vocabulary, much less the basic concepts, to talk like that.
In the Secret Life of The Sun (http://www.bbc.co.uk/programmes/b03694kd), a popular science program, I remember they gave a range of between 10,000 and 1,000,000 years and mentioned 100,000 as the average later in the programme.