The nature of a puzzling high-temperature ferromagnetism of doped mixed-valent vanadium oxide nanotubes reported earlier by Krusin-Elbaum et al., Nature, 431 (2004) 672, has been addressed by static magnetization, muon spin relaxation, nuclear magnetic and electron spin resonance spectroscopy techniques. A precise control of the charge doping was achieved by electrochemical Li intercalation. We find that it provides excess electrons, thereby increasing the number of interacting magnetic vanadium sites, and, at a certain doping level, yields a ferromagnetic-like response persisting up to room temperature. Thus we confirm the surprising previous results on the samples prepared by a completely different intercalation method. Moreover our spectroscopic data provide first ample evidence for the bulk nature of the effect. In particular, they enable a conclusion that the Li nucleates superparamagnetic nanosize spin clusters around the intercalation site which are responsible for the unusual high-temperature ferromagnetism of vanadium oxide nanotubes.