In the gemara R' Ashi explains that although typically one would need to raise an object 3 tefachim off the ground (to break the din of lavud) in order to make a kinyan on it, one can acquire an object in reshus harabim to be considered his and be chayev for damages even without lifting it 3 tefachim. However, this is only if one intends to acquire it, but if one does not intend to acquire it they will be exempt since they did not place the object there to begin with, but rather it was there from before. The question is what type of kinyan can be made by lifting the object less than 3 tefachim and having intent to acquire it?
Rashi implies that since there is an opinion who holds that a hefker object can be acquired through "habata" - looking at it, although we reject this opinion, we see that it is easier to acquire a hefker object than it is to acquire an object that is owned by someone else. Therefore, although one may need a hagab'ah of 3 tefachim for a standard hagba'ah, it is not necessary for a hefker object.
Tosafos also mentions this approach. Tosafos also mentions the possibility that the shovel which is the vessel of the person shoveling, can acquire for him without a hagba'ah, when he has intent to acquire it. Also, when one picks something up with their hand, they acquire it even within 3 tefachim of the ground.
Perhaps we can offer another approach. The gemara is working with the assumption that one is chayev for being mafkir his bor - meaning, that even if one does not own the object they can be chayev for bor. Therefore, it is possible to suggest that although normally one would require a standard kinyan to acquire the zevel of hefker, that is only to make him a full fledged owner. Here where he is merely acquiring it to be chayev for it's damages, even lifting it a little with intent to acquire would make him responsible for the damages that it causes.