Yes it is fully true that the real martyr is alive with Allah and his body does not rot. There are hundreds of cases witnessed by people when graves of martyrs were accidentally broken and the body of the martyr was seen fresh after hundreds of years of his martyrdom. There cases have been mentioned in many books. Recently when the grave of Hijr ibn Uday who was killed by Mo'awiyah in Syria was broken, people saw his body fresh after about 1400 years of his martyrdom. This is one of many other real cases.
'A book was published recently mentioned over 500 real similar cases.
Wassalam.