Just to be clear on your facts.  The taxpayer had physical silver bullion on deposit with a trustee.  She then moved the silver from the trustee to her personal possession.  The trustee issued her a 1099-R for sending (distributing) her the silver.

What does "She per her own investment into the IRA" mean.  It would truly be unusual if she put some else's investment into her IRA.  Are you trying to say that she made a non deductible contribution to her IRA?

What do you mean by "the basis of her silver has gone up"? I cannot imagine how that could happen.  Did you mean the the value of the silver has gone up?

"They are saying that the full amount is taxable" By they, I assume you mean the IRA trustee is reporting on the 1099-R that it is fully taxable.  I would not expect an IRA trustee to know if a taxpayer made a non deductible contribution to an IRA.

Distributions from an IRA are not required to be "realized" as in sold in order to be taxable.  Merely having unfettered access is enough.

Here is an article that seems relevant to your question:

https://www.thetaxadviser.com/issues/2022/feb/taking-possession-coins-irs-taxable-distribution.html