Good post above by
@Classof83. The VA can define veteran status, and veteran benefits eligibility, which is their prerogative. Each state has its own veterans affairs, veterans department, or veterans agency, which also defines veteran status and associated benefits for their state residents They can and do differ from Fed DVA. Many states are less strict.
Enlisted personnel categorized as active duty and entry-level status, and I believe the period is 180 days (I have not recently checked a primary source), encounter the same lack of veteran eligibility, though they are most definitely active duty, subject to the UCMJ, orders, etc.
Someone can be on active duty in training status, or duty under instruction, during that critical entry period, but that does not necessarily mean they will be eligible for full or partial DVA benefits if they separate before the end of the designated period. Much depends on type/reason for separation. There are reams of instructions on this.
Budget issues and precedent play a large role. Providing lifelong benefits to someone who was AD for less than X - it's a utilitarian decision to draw a line somewhere.