It's very odd to phrase it as "tensile strength", but capillary action is an expression of surface tension, which is the result of molecular cohesion--two (water) molecules resisting separation. In other words, strength under tension, with measurable stress and strain. With some squinting, you've got tensile strength with elastic deformation.
I think you are right and that is what they are getting at, but it is more a property of the system, not thee material. It is hard to reconcile fluid flow of a liquid with tensile strength.
[1] https://www.nature.com/articles/nphys2475