This is very strange if not unethical. Here are the terms. Its says nothing about company owned locations
Offer valid for qualifying stays at any La Quinta Inns & SuitesTM locations in the U.S. or Canada defined as follows; (i) check-in between March 1, 2018 and June 30, 2018 (ii) pay a room rate that is eligible to earn points per stay in the La Quinta Returns program, which are most rates available to the general public, including Best Available Rate, AAA, and AARP; (iii) at time of check-in, state that you want to earn Amtrak Guest Rewards points in lieu of La Quinta Returns Points and provide both your La Quinta Returns and Amtrak Guest Rewards member numbers. Guests must be a member in both La Quinta ReturnsTM and the Amtrak Guest Rewards program to earn points per stay. A stay is defined as one or more consecutive nights at the same hotel, even if intermittent check-in/check-out events occur. This offer is available for one room only, and cannot be combined with any other offers, discounts or promotions and is non-transferable. Please allow 6 – 8 weeks after check-out for your points to post to your Amtrak Guest Rewards account. All La Quinta Returns program terms and conditions apply; for details, please visit LQ.com/Returns. All Amtrak Guest Rewards terms and conditions apply.