A photon traveling from its source at light speed is said to not experience time and therefore be everywhere at once.
By whom is this said?
Can you provide a link to an authoritive source?
The reason I ask is because what relativity and QFT tells us is that there is no meaningful way to talk about the reference frame of a photon.
The sentence suggests a misunderstanding of time dilation too ... so it is hard to know what the author is trying to say without access to the reference.
Well not exactly, it can only be everywhere at once along its projected path assuming the photon's path in a vacuum is not altered by anything.
Similarly - the trajectory of a photon is not a well defined concept.
The "photon" belongs to quantum models where position and momentum are uncertain. Photons are understood in terms of probabilities.
In Relativity, we do not use photons.
Time itself cannot alter the path.
Time is a dimension, not a force.
But, by definition, nothing can alter the path of anything. The path that something takes is the path that it takes.
Gravity however, affects both time and space and therefore could alter the path of a photon that exists everywhere at once along a path unaffected by time. Is this correct?
As you are probably figuring out, the short answer is "no". But only because it sounds too confused to give any other answer.
Curvature of space-time
is gravity - not an effect of gravity.
In GR, all light rays are straight lines in space-time. The curved paths for light in gravity is an artifact of the observer's reference frame - which is no longer inertial..