You've been doing the right thing, Liam's Mom: asking questions, educating yourself, and especially seeking another doctor's opinion.
Liam's symptoms certainly sound like aplastic anemia, and getting a definitive diagnosis is necessary to know what treatment is most appropriate. You should not have to put up with evasiveness from Liam's doctors. You might ask them why they have any doubt about Liam having aplastic anemia.
If you haven't already done so, I recommend that you get the information packet offered by the Aplastic Anemia & Myelodysplasia Association of Canada (AAMAC). They describe their services, and give contact information, in the
Welcome from AAMAC thread, and they encourage patients and family members to seek each other out, as you've done by coming to Marrowforums.