Yes - Medicare is typically lower than private insurance plans, but if you can't deliver care for the reimbursement that Medicare offers as a health system/plan/office/provider, you're probably overcharging.
More than that, Medicare is the de facto starting place for most reimbursement negotiations between providers and payers. One of its benefits is that it's transparent and readily available. Blue Cross isn't gonna tell you what it's contracted to pay an individual provider (and that individual provider often won't know what they'll be reimbursed untill after they submit a bill) - but with Medicare the data's out there.
I know a good number of private clinics that'll offer cash pay discounts that effectively mirror Medicare or even slightly below Medicare, since you're saving them the trouble and expense of going through the medical billing process.