Altruistic behaviour can be defined as behaviour that benefits another organism not closely related while apparently detrimental to the organism performing the behaviour, benefit and detriment being defined in terms of contribution to inclusive fitness.
Note the last section - about inclusive fitness. In systems whose evolution has been influenced by group selection or kin selection agents act to increase their inclusive fitness. They are not behaving atruistically.
It is possible to define altruism without measuring costs and benefits in terms of contribution to inclusive fitness - but such definitions are not of very much use. Inclusive fitness is the currency of evolution - its natural yardstick.
Reciprocity isn't much use in explaining altruism either. Though many insist on calling it "reciprocal altruism" it isn't a form of altruism at all.