Where does it state in the FAR that the KTR must bill costs at the CLIN/ACRN level?
I think the answer to your question is located in FAR Clause 52.232-25. Specifically, paragraph (a)(3) reads as follows:
(3) Contractor's invoice. The Contractor shall prepare and submit invoices to the designated billing office specified in the contract. A proper invoice must include the items listed in paragraphs (a)(3)(i) through (a)(3)(x) of this clause. If the invoice does not comply with these requirements, the designated billing office will return it within 7 days after receipt (3 days for meat, meat food products, or fish; 5 days for perishable agricultural commodities, dairy products, edible fats or oils, and food products prepared from edible fats or oils), with the reasons why it is not a proper invoice. The Government will take into account untimely notification when computing any interest penalty owed the Contractor.
(i) Name and address of the Contractor.
(ii) Invoice date and invoice number. (The Contractor should date invoices as close as possible to the date of the mailing or transmission.)
(iii) Contract number or other authorization for supplies delivered or services performed (including order number and line item number).
(iv) Description, quantity, unit of measure, unit price, and extended price of supplies delivered or services performed.
(v) Shipping and payment terms (e.g., shipment number and date of shipment, discount for prompt payment terms). Bill of lading number and weight of shipment will be shown for shipments on Government bills of lading.
(vi) Name and address of Contractor official to whom payment is to be sent (must be the same as that in the contract or in a proper notice of assignment).
(vii) Name (where practicable), title, phone number, and mailing address of person to notify in the event of a defective invoice.
(viii) Taxpayer Identification Number (TIN). The Contractor shall include its TIN on the invoice only if required elsewhere in this contract.
(ix) Electronic funds transfer (EFT) banking information.
(A) The Contractor shall include EFT banking information on the invoice only if required elsewhere in this contract.
(B) If EFT banking information is not required to be on the invoice, in order for the invoice to be a proper invoice, the Contractor shall have submitted correct EFT banking information in accordance with the applicable solicitation provision (e.g., 52.232-38, Submission of Electronic Funds Transfer Information with Offer), contract clause (e.g., 52.232-33, Payment by Electronic Funds Transfer-System for Award Management, or 52.232-34, Payment by Electronic Funds Transfer-Other Than System for Award Management), or applicable agency procedures.
(C) EFT banking information is not required if the Government waived the requirement to pay by EFT.
(x) Any other information or documentation required by the contract (e.g., evidence of shipment).
Bottom line: According to the Prompt Payment Act clause, a proper invoice must include the line item number.