Historically, a veteran eligible for VA benefits who hasn't actually received VA benefits in the last three months can still be eligible to make or receive HSA contributions.
Effective January 1, 2016, The Surface Transportation and Veterans Health Care Choice Improvement Act (H.R. 3236) permits veterans enrolled in a HDHP (without any other disqualifying coverage) and who have a service-connected disability to make or receive HSA contributions regardless of when they received VA benefits.
There was previously a rule regarding medical benefits received in the previous 3 months but it is no longer effective and does not apply.
Source: IRS Notice 2004-50 Q&A Q-5