Reservists who are activated, even if they are housed by the military during their mobilization, are still paid BAH on the assumption that a reservist still may have the civilian obligations (like a mortgage) that BAH is designed to offset.
ɹɪzˈɜːvɪsts hˌuː ɑːɹ ˈæktᵻvˌeɪɾᵻd, ˈiːvən ɪf ðeɪ ɑːɹ hˈaʊzd baɪ ðə mˈɪlətˌɛɹi dˈʊɹɹɪŋ ðɛɹ mˌoʊbɪlᵻzˈeɪʃən, ɑːɹ stˈɪl pˈeɪd bˌiːˌeɪˈeɪtʃ ɔnðɪ ɐsˈʌmpʃən ðˌæɾɚ ɹɪzˈɜːvɪst stˈɪl mˌeɪhɐv ðə sɪvˈɪliən ˌɑːblɪɡˈeɪʃənz lˈaɪk ɐ mˈɔːɹɡɪdʒ ðæt bˌiːˌeɪˈeɪtʃ ɪz dɪzˈaɪnd tʊ ˈɔfsɛt.