Nope. Manufacturers can impose different limitations based on operating requirements or other aircraft equipment, which is called an operational ceiling. The person who you quoted from Quora conflated the issue and based on the FAA definition, the answer was only partially correct. The language used to describe a service ceiling may be what the manufacturer calls it, but it is not, by FAA definition, the service ceiling.
By the FAA’s definition in the Pilot’s Handbook of Aeronautical Knowledge, the service ceiling for a piston aircraft is reached when it can no longer sustain a 100 fpm climb, the altitude of which, as discussed, is variable and primarily dependent on weight and density altitude.
But your quote is missing the point entirely. If you defined the service ceiling as 300fpm, then the service ceiling altitude would actually be much lower.
Here’s the climb rate chart for the Seminole, so you can see that it’s dependent on pressure altitude and temperature (density altitude), and weight (and, of course, it’s not going to be 100% accurate, every time, every plane, but close enough):
