I believe your understanding is correct. To use United terms, you would need $4,000 PQD (=20,000 points - it's the same exclusion of fees that UA uses for PQD) on VX tickets to be Silver, and can supplement that with up to 15k points from the CC and/or distance-based earning from flying VX partners. No component of VX elite status depends directly on BIS miles flown on VX.