As the volatility increases the price of a callable bond decreases and hence one would think the rate used to discount the time values in a binomial model should be higher whcih would mean higher option adjusted spreads.
You’re misinterpreting the statement. They’re not saying that actual volatility increases. They’re saying that the volatility used in the binary tree model increases.
As (model) volatility increases, the call option is more likely to be exercised, so the average cash flows will be lower. To discount lower cash flows to get the same market price requires a lower discount rate, thus a lower OAS.
If they were 4% and 5%, then the average would have been 4.5%.
If they are now 3% and 6%, the average is still 4.5%…when you are using the binomial tree for backward induction on an option free bond, I believe the 4% and 5% will give you the same output as the 3% and 6%.
Now you are discounting one cash flow by a higher amount, but another cash flow by a lower amount - averaging out to the same.