There's no rule saying you can't collect in summer, but you have to keep the tree's needs in mind, as the needs are different in summer rather than spring.
First, you have to consider how much time there is before winter. Collected trees can take months to sprout a single shoot, so a mid-summer collection will have a higher chance of survival if you leave some foliage. This will give it a chance to store up energy to survive the winter.
Second, you want to avoid a huge root disturbance so that the foliage you leave has an adequate water supply.
In order from bad to worse for a hot, mid-summer collection:
Small foliage, lots of feeder roots
No foliage, lots of feeder roots.
No foliage, bare roots.
Lots of foliage, bare roots. (This is the worst because the tree will expend precious energy trying to save the leaves, but will fail, in which case you're now in situation 3 but will less in the tank).
Collecting in the fall or early spring is more ideal because you don't have to worry about these things and can be much more aggressive with root work and hard chopping.
