They don't give a reason. I don't believe the author. I think it will not only technically work fine, but it's a good idea and better than using what the author suggests.
It's not worth the effort to break mDNS because lots of apps can use mDNS, it's a useful standard. In fact, in many LANs today (on modern operating systems inc. relatively recent versions of Windows 10 as Microsoft was one of the last to adopt mDNS) mDNS does almost everything people would want DNS to do in LAN scope anyway and you could get away with not assigning any local DNS and just using mDNS services.