Lightning is complicated and I don't think there's a simple, straightforward answer to this. I found a really detailed paper about this and it has a lot of detailed content while also being relatively easy to follow. I encourage people to read the full paper here: The physics of lightning. I found it really informative and helped disabuse me of my own incorrect notions.
First off, the most lightning never reaches the ground:
All lightning discharges can be divided into two categories: (1) those that bridge the gap between the cloud charge and the Earth and (2) those that do not. The latter group as a whole is referred to as “cloud discharges” and accounts for the majority of all lightning discharges.
The question is about lightning strikes that might strike a person, who is presumably on or near the ground so we can focus on the minority: category (1) above.
Summarizing from the article:
- About 90% of cloud-to-ground lightning flashes are initiated by a negatively-charged, downward-propagating leader
- About 10% of cloud-to-ground lightning flashes are initiated by a positively-charged, downward propagating leader
- The remaining two types of cloud-to-ground (actually ground-to-cloud) lightning discharges are relatively uncommon and are upward initiated from mountaintops, tall man-made towers, or other tall objects, towards the cloud charge regions
The last point is interesting, I think, but upward lightning is rare and wouldn't typically be a risk to a person unless they were on one of these objects, and I think most people understand that the top of a cellphone tower during a lightning storm is a risky place to be. So we can ignore those as well. This leaves the 'downward strikes'. For brevity, we will also ignore the less common positive 'downward strikes' and focus on the most common cloud-to-earth strikes:
The physical mechanism for moving the negative charge to Earth is a propagating electrical discharge called the “stepped leader”.
This is mechanism is explained as:
The stepped leader’s movement from cloud to ground is not continuous, but rather it moves downward in discrete luminous segments of tens of meters length, then pauses, then moves another “step”, and so on.
Presumably, this gives lightning its characteristic zig-zag appearance. Skipping ahead, we get to the part that is relevant to the question:
When the stepped leader is near the ground, its relatively large negative charge induces (attracts) concentrated positive charge on the conducting Earth beneath it and especially on objects projecting above the Earth’s surface.
The key word 'attracts' appears but to be clear, it is not saying that the objects attract the lightning, but rather that the nearing negative charge causes the ground and objects on the ground to become net-positively charged. To understand this, it's crucial to understand that the earth is, in general, assumed to have a neutral charge. That is, negative and positive charges are balanced. When a large negative charge comes near the ground, that balance is disrupted as the negative charges in the ground are repelled and positive charges are attracted.
When the electric field intensity near ground from these charges becomes large enough, upward-going, positively-charged electrical discharges from the ground or from grounded objects will be initiated, ... One of these upward-going discharges will contact a branch of the downward-moving leader, thereby determining the lightning strike-point and the primary lightning current path (channel) between cloud and ground.
That last bit is important here. The final path to ground is determined by which object or point on the ground initiates the upward positive discharge. So it makes sense that an object that is taller is likely to be closer to the downward leader, in which case, the field strength will be stronger at points on that object that at the ground surface.
And finally:
Understanding the “attachment process” is critical to the proper design of lightning protection systems. Unfortunately, the attachment process is sufficiently complex and variable that it has not been possible to gain more than a relatively crude understanding of it.
So, the answer is complicated. Logically, though, conductivity of the object(s) in question would influence how easily an 'upward-going discharge' will be initiated through that object. So, while the initial claim may not be strictly correct, I think saying it is strictly false is more wrong. Holding a aluminum pole over your head in a lightning storm might be more dangerous than holding an insulating pole of the same length but neither is advisable.