ANSWER:

What they say is correct. For Hajj the male mahram accompanying women is required even if it’s not a traveling distance. 

She’s sinful for not making hajj with her male mahram but the hajj is valid.

My mom did her Hajj in days when we were settled in Jeddah . She went without mahram.My Dad was with us kids in Jeddah. she was told from Jeddah to makkah is not a travel so can do so. But nowadays everyone tells her what she did was wrong and that for hajj mahram is compulsory. Kindly shed the correct view.