By and large the article is correct.But there are certain manthrs given by God himself,which any body can recite with benefit.These do not require manthra diksha from a Guru.Here guru Himself is Bhagvan.Some of such mathras are given below:-
1.Om Namo Narayanaya Nama
2.Narayana
3.Hari
4.Hare Rama Hare Rama Rama Rama Hare Hare
Hare Krishna Hare Krisna Krishna Krishna Hare Hare
5.Om Nama Shivaya
Number times normally 108 and multiples thereof.
Click here for the article
-P.M.G.Nampoothiri, Thiruvananthapuram,