It's more than a few years since I took, and hated, the law school course in labor law. I don't recall off-hand the name of the statute, but there is a federal law requiring contractors on a federal construction project to pay all workers the prevailing union wages irrespective of whether they are union members. Thankfully, my recollection of that is vague and I've never touched an issue even close to involving labor law.
Found it---It's the Davis-Bacon Act
This section includes the answers to several of the most frequently asked questions about administration of the Davis-Bacon and related Acts.
Section A
INTRODUCTION
THE DAVIS-BACON AND RELATED ACTS (DBRA)
The Davis-Bacon Act as amended, requires that each contract over $2,000 to which the United States or the District of Columbia is a party for the construction, alteration, or repair of public buildings or public works shall contain a clause setting forth the minimum wages to be paid to various classes of laborers and mechanics employed under the contract. Under the provisions of the Act, contractors or their subcontractors are to pay workers employed directly upon the site of the work no less than the locally prevailing wages and fringe benefits paid on projects of a similar character. The Davis-Bacon Act directs the Secretary of Labor to determine such local prevailing wage rates.
You are correct. That clause is in every Federal, State of IL Bid Document Package / Specifications. Some localities like Park Districts, insert it too and many regular commercial type project AIA Bid Packages have it also.
I could grab a Spec, one of many I have laying around, and cite it chapter and verse, but I have some 'stuff' to do soon. But you're correct.