Technically, it is not a forgery. It is a reproduction. A forgery is intended to deceive the buyer. A reproduction may only be sold, for example, as a souvenir. It's like when a tourist goes to Paris and they sell the little Eiffel Towers--no one feels cheated when he gets home and a friend tells him it is not THE Eiffel Tower. Many reputable museums and other dealers sell clearly identified reproductions (with an R or the word "copy" somewhere on it) to those who like the coin but cannot afford the real thing. Your grandmother was probably told that story, and she merely repeated it to you.
You asked "Real or Fake"? I think it's clear, between these two options. The letter "R" stands for "Real". I used to own one too, as did AncientJoe. See attached pic. Sadly it lacked the "Real" mark. And was quite worn. Joking aside, relatively speaking the type isn't that rare. There's probably 20 to 50 Roman Republican denarii types that are much rarer than an EID MAR. Not btw including the Cleopatra denarius. Ted Buttrey once outlined his reasoning for thinking the Cleopatra denarius type was struck by over 500 dies which would make it one of the most common denarius types known. It's however dispersed over a great number of non-specialist collections, most which will never be marketed as collections of ancient coins. And it's consistently desirable. So it seems rare. But it isn't.
brutus was a cheapskate too. I think his genuine ones were lower grade silver than most republic denarius
Modern fake. It looks like it is a struck coin and the metal is right but the style is wrong. Here's a match in Forum Ancient Coins' fakes gallery:
Mine's on an oversized flan, as it was apparently overstruck on some kind of tetradrachm with an eagle reverse.
In my limited experience as a coin dealer, I've been presented with supposed Spanish treasure cobs ("pieces of eight") which came with similar family heirloom backstories, or metal detecting tales (and real beach sand in the crevices). But the "coins" have invariably been modern gift shop replicas made for tourists. Not all of these people were trying to pull a con job. Some might have believed the stories they had been told. And the beach find might have actually happened- just with a fake coin. As a detectorist, I've dug replica items in historic places, myself- right next to authentic ones. Being dug doesn't automatically make something old. Then again, I live in an area where real finds do occur. My local detecting buddy found this. *Admittedly, not too many EID MAR denarii have been unearthed in coastal Georgia, USA. I did find a real Roman coin once, though.
I'm not able to find it anywhere now... I purchased a copy off of eBay after hearing it was being produced a handful of years ago but then I heard that the printing was unauthorized and there was some controversy around the whole situation. I'm not finding it anywhere now so I'm guessing it's being "revised". My copy is in storage at the moment but I'll dig it out the next time I'm excavating volumes.
Rule of thumb: If you find an extremely rare coin from a dead relative, or a relative gifts it to you, or on eBay for a ridiculously low amount, 99% of the time it's a forgery or it's misatributed and it's actually a fairly common coin. Sure, surprises can happen. I'm sure some relative of mine will have a blast one day after I'm dead when they open my collection and see tens of thousands of dollars worth of ancient coins, but stuff like that doesn't happen every day. Reminds me of people who try to pawn or sell their dead mom's mid-20th century blue vases and plates which were acquired in some UK trip in the 50's or 60's. They think they have a fortune until they walk into some antique shop and find the place bursting with the same exact stuff. Turns out the rare family inheritance is just some common tourist items that just about every American brought back from their overseas trip. For every 100 of these cases that turn out to be nothing special, you may only have 1 who has some genuine treasure such as a Picasso vase or other such valuable.
How many of us have a plan in place telling heirs what to do with our collections? I have twice told my wife what to do if I turned up dead only to have that dealer drop out of the business. Today I am seeking another one but fear causing them to go out of business. The vast majority of my coins were bought from sellers older than I am. Will they be available when my heirs need them? Not every dealer is interested in marketing mid level collections; every dealer wants the top 5%. Finding a good fit in price bracket and timing is not all that easy. Not doing anything can result in the coins grandpa bought for $100,000 to $1 million going to a flea market with those blue plates.
I hope to God that my collection does not end up selling with those blue plates at the flea market. But I have a bad feeling that many may never be appreciated again.