Strictly speaking $r$ doesn't refer to the tube at all. It is the radius of the 'base' of the droplet (the base being the circular area where the droplet is attached to the capillary tube).
For a well designed tube the rim of the tube is hydrophobic, it repels water, causing the droplet to detach from the rim while hanging, thus having a base equal to the internal tube. In that case $r$ is indeed equal to the internal tube radius.
However, for a rim of the tube that is wetted by water (like the one you've drawn in your question) the $r$ can basically be anything between the internal radius of the tube and the external radius of the tube, as determined by the contact angle of the water with the rim. Indeed, as mentioned by @PhotonicBoom, for a tube with a very thick wall it will never be the external radius, but for a thin tube it is certainly possible.