Alberto Fresneda Carrasco, 19, and Jack Gilbert and Harrison Scott-Hood, both 23, were killed last year as they crept down the tracks near Loughborough Junction station, south London.
It is thought they were struck by a train at 1:16am on 18 June 2018.
Speaking before an inquest into their deaths, their families gave a joint statement defending graffiti – saying it was an "amazing art form".
They said: "Eight months ago our sons: Jack Francis Gilbert, Alberto Fresneda and Harrison Scott-Hood, three young men with a love for life, promising futures ahead of them and a passion for art – particularly tagging – tragically lost their lives because of the dangerous risks this art form brings.
"The 'painting community' take their art seriously in trying to find a status. This passion is what brought our boys together.
In a time full of needless violence, if our sons were guilty of anything, it was their love for painting
"In a time full of needless violence, if our sons were guilty of anything, it was their love for painting.
"We can only express to young people trying to make their mark, to please be safe. Keep your creativity alive – but don't risk your lives."
The grafitti artists – dubbed The Three Musketeers – were struck by a train near Brixton station and could only be identified through their fingerprints.
Tributes from street artists flooded in for the tragic trio – including a mural featuring the three men's graffiti tags: 'Lover', 'K-Bag' and 'Trip' on the side of a Tube train.
Giving evidence, Jack's mother Maxine told the coroner: "From an early age Jack loved to draw or paint.
"At home when he was relaxing, he was always scribbling away in his art book.
"His talent was recognised at school when he was picked to paint a mural ironically outside the local train station.
"He did private art work and was paid to design shop fronts.
"Painting grounded him and in those last few months, in our family's darkest days, it was his release. For that I will never condemn my son for what he did."
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