Is income contributed to a 457(b) subtracted from the earned income limit for an IRA?

My wife and I are over age 50.

My wife had earned income from a job of $43k, and contributed $30k to a 457(b).

Now we want to max out our IRAs as well, at $8k each.

The IRS publication 590-A says my contribution is limited to:

1. The total compensation includible in the gross income of both you and your spouse for the year, reduced by the following two amounts.

   1. Your spouse's IRA contribution for the year to a traditional IRA.

   2. Any contributions for the year to a Roth IRA on behalf of your spouse.

No mention of workplace plans.  So, my reading of this is that my contribution is limited to the gross income ($43k) minus her contribution ($8k), which allows me the full contribution ($8k) for myself.

But this doesn't seem right, because we would basically be putting $30k plus $16k in taxed advantaged accounts, which is more than her earned income.  I can't find anywhere that it mentions workplace plans in connection with IRA limits.  Am I understanding this right?