Larcher,
if we are talking about Roe deer, your friend is broadly right. Velvet should be shed by the end of May but this can be affected by many things. If it is cold in April/May as it frequently is in the UK, fraying or shedding may be delayed and the velevet can become hardened on the antlers making it difficult to remove. Although your friend cannot state it will always be done by 1st June, in most cases, it will be.