clearlycanadian

Not sure what notes you’re referring to. The CFA material is pretty clear (well, if you read between the lines ) about using the issuer’s on-the-run yield curve for the binomial model. Also, the term “treasury bond” is used loosely. For bond valuation, we use the spot rate curve (AKA term structure of interest rates) derived from zeroes.
When I was on the valuation reading, I actually had to go back to some of the level 1 material to figure out what was going on with the interest rates:
You start with the bond’s YTM.
Use YTM to derive spot rates (level 1 material).
Use spot rates to derive forward rates (level 1 material). The rates in the binomial tree are forward rates.
If OAS is introduced, it is added to each forward rate in the binomial tree to value the bond.
The market value is determined the same way it is for any other security… people trade. If we could value this crap with certainty, we’d be Gods on Wall Street, man! The CFA material even has examples covering the uncertainty of valuation models - one dealer may quote a lower rate than another, all because they used differing assumptions (volatility, their selection of on-the-run issue, etc.).