Alexander was also quite sure that Philip may have been bending the truth at least a little to protect his friend, but considering the younger boy was in agony on the ground, it really wasn't the moment to push Philip on the matter. Perhaps he would ask him later, perhaps it didn't matter really. If Philip was covering for his friend, it was an admirable display of loyalty rather than a cowardly lie.
Philip listened intently as Mr Black told him there was an important task for him to complete. It sounded a little silly, and perhaps on some level he was aware that he was being fobbed off, but he wasn't the sort of child who disobey or question a direct order from an elder. "Yes, sir!" he told him with determination. "I'll be back in a minute, Sirius!"
Although Alexander wasn't about to run off and leave them to it, he was very much allowing Arcturus to take the lead. If he asked for help, or seemed to really be struggling with something, of course he would offer his assistance, but to him Arcturus was Sirius's guardian. It may have seemed strange to the more modern sorts, but that didn't meant that they were right.
He also saw no reason to call for a doctor, or rush him along to medbay. If Arcturus had no such painkiller for him, they would call Neville for a potion, that was what Black would want, wasn't it?
"Yeah, of course I will," he nodded, following him toward the house, staying close just incase he couldn't manage the whole way alone.