The issue is that folks claim this, but there is no data out there to support it - it just seems like a perception. There is always a bias in the saying "you get what you pay for" - it's not universally true and people overpay for many things and equate higher cost with more value, better service, etc.
Talk to most motel franchise operators and they'll relate their own horror stories regrading booking sites such as Expedia, Travelocity, Hotels.com, etc.. If you're in the travel industry, you're reliant on booking sites and positive reviews, people will always chase the lowest possible price. What CAN happen is those customers may inadvertently feel the frustration of the property owner and their displaced anger. To the OP, if you're booking using your Ultimate Rewards points, you should be fine, Chase and Expedia are major partners and one isn't going to risk disappointing the other's members due to poor service. Just review the trip insurance booking coverage your card has.
As for the perception that higher cost = better service/location/amenities, in the most general sense, it's true, however, you've got to know the difference between properties/services and weigh it against your priorities. Are you paying more because of more sq footage, nicer bath, location, A/C, same size room but quiet section, etc...