Yes, measured by compression or tension in just the right way, many structurally appropriate bamboos are about 11.2 times stronger than steel.  But let us take a closer look.  The illustration below defines important parts of a bamboo pole.

The internode  is where the bamboo is strongest in compression and tension.  This is where the test for strength is taken.  The node is not as strong.  The strength of the bamboo is very directional.  The fibers are bundled within the internode parallel to the axis of the pole.  These fibers and their surrounding lignin and other materials resist being compressed and stretched very effectively in the internode.  However, the vascular bundles and some of the fiber turns at the node and passes through the disc of material at each node called the septum.  If the test is run with the node under stress, failure will occur at a much lower value.  Even more important, the calculation is made based on weight.  That means that one kilogram of steel tested against one kilogram of bamboo yields the ratio of strength 11.2 in favor of the bamboo.  Steel is dense (about 7.859 g/cm² ), and bamboo is not dense (about 0.5 g/ cm²).  In addition, bamboo is hollow.  The area compressed is a ring, not a circle.  For example, a one centimeter diameter rod of steel weighs the same as a 4 cm diameter bamboo with a 2 cm wall thickness.  A strip from that bamboo about  1 cm long will support the same load as the 1 cm diameter steel sample. This is a good showing for the bamboo.

The weakest direction of bamboo is perpendicular to the axis and tangent to a circle on or within the wall.  Many applications of bamboo do require splitting the bamboo, making this tangential weakness a real blessing.  The fibers of bamboo can be pulled apart from each other easily.  Between the strength of longitudinal compression and low tangential strength is the shearing force, when the fibers resist sliding past each other in direction that they grow.  The ability to withstand twisting forces is fair.

There are about 1500 species of bamboo.  Some are much stronger than others.  Bambusa asissi and Dendrocalamus strictus are extremely strong.  Guadua is extremely tough. Some herbaceousbamboos are no stronger than reed.  Some bamboos have very thin walls but grow to larger diameters.  Matching the bamboo to the application makes for greater success.  Bamboo is a great building material for fences and many other structures, but we should have reasonable expectations.