Well, if he could do it from his side of the fenceline, sure he can. But he probably needs to go onto your property, and obviously he can't do that without permission.
That's consistent with the existing legislation.
Since 2011, the laws in Queensland has changed. Broadly, "tree keepers" are required to keep their trees from causing a nuisance to neighbours, at their expense.
This Queensland government page includes a link to the 2011 legislation.