Webopedia isn't a good source. You might want to find someone who has actually worked with these, like me.
The fact it can be erased does not change the fact it is Programmable Read-Only Memory.
You cannot take a PROM and make it erasable. You have to develop a completely new device using a completely different technology in order to develop an EPROM. One is not derived from the other. They are completely separate.
Who said you could?
Question: Is a PROM, Read-Only Memory(ROM)?
Answer: Yes
Question: Is an EPROM Read-Only Memory(ROM)?
Answer: Yes
Question: Is an EPROM Programmable Read-Only Memory(PROM)?
Answer: Yes
For your position to be correct, you must answer "no" to all of those questions. Are you ready to take it to that level - complete absurdity.