In regards to their actual climbing of trees, one might well imagine a technique similar to the pacific islanders means of ascending coconut palms, only with the added advantages of longer arms, more flexible feet(with"active"toes), bigger hands, and seemingly tremendous upper body strength, all of which would better enable the behavior.
An earlier post mentioned the aspect of weight distribution to offset body mass/branch capacity issues, which makes perfect sense, especially in light that these creatures are climbing virtually all of their lives, so they probably have a pretty good idea of how not to break a tree, or at least how to choose the ones least apt to break under their weight.
Some have discredited the idea of the big furries using trees for refuge, escape pathways, hunting and such based on the idea that since they are apex predators of great strength, considerable speed, and an overall hugeness, they have no need for such additional behaviors or abilities. Presuming a cognitive intelligence, they would surely recognize the benefits of additional options of recourse within a given environment,contributing to their versitily and capacity to respond to whatever situation may arise.
To state that "if they climbed trees we would already have a type specimen" is evidence of limited consideration, for it is those creatures with limited evasion behavior options that prove most predictable, and therefore easier to capture or document, rather than sentiently adaptive creatures with a greater number of options from which to CHOOSE their responses, thus enhancing their ability to function effectively within their environment and evade predations.