Lelanya, I don't think that's correct. I'm in a FS that had put the Spire Perks up to level 3 & eventually banked the maximum of 150 Spire points. The next month the AM used the free Reset and re-did the Perks, leaving the Spire Perk at 0 this time. Fast forward and yesterday we were short a player so the AM was able to spend some of those previously banked points to get us the next Spire FS chest even though the Spire Perk was still showing level 0. What we can't do at level 0 is replenish the bank. If we still have 51 points in the Spire bank, we'd have to go back to Spire Perk level 2 in order to bank any because level 1 only lets you bank up to 50 & we're already there; level 2 lets you bank up to 100.
But yes, you can spend banked points even if your Perk level is now 0.