If the point of hiring a well established, experienced, reputable painting contractor is to secure the professionalism and trust suggested to be inherent with that choice, then I would EXPECT that professionalism and experience to include the ability to make the proper and correct calculations for labor and materials for a fixed price quote, and there should be NO reason for the contractor to put the cost burden of their miscalculation on the consumer.
"I had called the last minute for an interior painter, because I had flown into town for just 5 days, to get my home painted. PPP Paint Services made time for me. Made an appointment on a Monday and they were there by Thursday and done by Friday. 9 rooms including trim work. The job came out great, and at a great value. I would highly recommend this company."
EPA's Lead Renovation, Repair and Painting Rule (RRP Rule) requires that firms performing renovation, repair, and painting projects that disturb lead-based paint in homes, child care facilities and pre-schools built before 1978 have their firm certified by EPA (or an EPA authorized state), use certified renovators who are trained by EPA-approved training providers and follow lead-safe work practices.
If a quote seems high, ask the contractor what is increasing the price point. Perhaps it's something that can be negotiated, or maybe this business is just overpricing their services. On the other hand, be skeptical of any price points that seem unfathomably low. There could be a reason their prices are below the industry norm - perhaps their quality standards are uncommonly low, too.