The ID check isn't for age verification. Federal law requires IDs to be recorded* to enforce restrictions on the maximum quantity that an individual is permitted to purchase per month.
* Edit: Where the word "recorded" appears, this comment previously said "scanned and submitted to a central database". While most states use a central database, the comment reply below pointed out that this goes beyond the minimum that federal law requires.
I am not aware of a centralized federal database. My understanding is that federal regulations stipulate that the pharmacy must see photo ID and take note of who bought the pseudoephedrine, when, how much, and keep that information logged either on paper or electronically. To be available to law enforcement on request.
The Oregon law does have a central database requirement, however I believe this is in all cases a decision made by each state individually.
You are correct, I was conflating two separate steps of the process. Federal law only requires keeping records and these could technically be done on paper. In practice, more than two thirds of the states participate in a central electronic database called the National Precursor Log Exchange.
* Edit: Where the word "recorded" appears, this comment previously said "scanned and submitted to a central database". While most states use a central database, the comment reply below pointed out that this goes beyond the minimum that federal law requires.