The incident with Garithos certainly didn't help relations, but it wasn't insurmountable. The BElves were still leaning towards siding with the Alliance, evident by them initially accepting Alliance ambassadors and snubbing Sylvanas' offers. They only accepted Sylvanas' help when it became clear the Alliance representatives were spies and they didn't really have anywhere else to turn to.
EDIT: However, when referenced, Blizzard usually goes to the Garithos incident because it is more well known and more poignant. Not everyone played through the BElf starting area.