I don't think this is hard to understand: those who make canonical vows are bound by (additional) canon law(s) in ways those who make private vows are not. Neither do the canon laws applying to such things apply to most Catholics. There are sections of the Code of Canon Law which apply to all baptized persons (cc204-231 and sections of the code on sacraments, on liturgy, etc.) but there are many more that apply to more specific segments of the Church: to clergy, to the married, to institutes of consecrated life and in some ways to canonically consecrated hermits, to consecrated virgins, to the teaching office of the church, etc, etc. Not every section of the law is of interest much less do they actually apply to every person in the Church. So imagine my surprise when the person who claimed a private vow of obedience was one of "canonical obedience" wrote the following:
[[A hermit colleague was upset by my mentioning that I render canonical obedience. Yes, I do. Any practicing Catholic ought render obedience to the various and multitudinous Canon Laws developed over the years. At least we ought to try just as we try to be obedient to civil laws on the books. Why not? The inclusion of my being obedient to my bishop in whatever diocese I may reside and to obey canon laws should not be a source of upset to others. Rather, we should rejoice at our human and flailing attempts to canonical obedience but even more so to obedience to Jesus' precepts, particularly that of God's Law of Love.]]
Of course "canonical obedience" does not mean simply being obedient "to the various and multitudinous Canon Laws developed over the years" (were that even possible or reasonable). It means being bound by the specific canons applying to those admitted publicly (i.e., canonically) to a vow of obedience. No more, no less. Those with private vows do not owe and are not bound by the canons applying to those with canonical (public) vows anymore than those publicly professed as religious are bound by the canon laws applying to marriage or vice versa. For that matter diocesan hermits are not (generally speaking) bound to obey canons applying to priests, or even all of those canons which apply to religious. Similarly, apostolic religious (again generally speaking) are not bound by canon 603 any more than they are bound by the canon law that applies to priests, those that apply to married persons or those that apply to bishops, to theologians, etc., etc.

The bishop is the legitimate superior of diocesan priests and diocesan hermits, for instance, because a qualified but undiminished expression of Christian freedom which is spelled out in both canon and proper law (e.g., the hermit's Rule) and which each has publicly embraced in either the rite of ordination or religious profession, exists between them. It is together that they will do the will of God within a specifically ecclesial vocation. Because there is no carefully delimited and mutually defined relationship where rights and obligations are similarly spelled out (in Rule and/or Constitutions) and embraced via public rite, the bishop is not the legitimate superior of lay members of the diocese and is not owed "canonical (or religious) obedience", nor should he be. This is so because such carefully limited and explicitly defined public relationships do not come to be through baptism alone, not even when entirely private vows are added to the mix.
To summarize the point here then, one cannot simply pretend to be bound to religious or canonical obedience in this way by referring either to the common obedience owed to one's bishop or to a host of laws one neither understands and which do not even apply to their lives. These members have the right and obligation to honor Christian Freedom in any way they discern in good conscience and so long as they do not transgress into areas of the Church which bring them under the direct purview of the bishop's authority, they are obligated to do so without the permission of the bishop or someone he delegates to oversee their activity. They have an obligation to submit their own wills to Christ's but neither is this is canonical obedience because these persons are NOT canonically vowed to the specific expression of Christian freedom and responsibility associated with public profession. To call it canonical obedience is analogous to calling a year of some sort of initial formation in a non-canonical community a "canonical year". In either case this usage is mistaken and literally incoherent.
The Relevancy of Canon 603:
Ms Joan McClure, the author of the position being discussed here and a privately vowed hermit and (vocationally as well as hierarchically speaking) a lay member of the Archdiocese of S______, does not owe Archbishop S______ "canonical obedience" and I am sure he would be the first person to explain to her that she does not. Ms McClure also wrote about my response regarding "canonical obedience": [[ If we get upset over desire to obey laws of the land and laws of the Church, or laws of God especially--this upset is an example of not letting Christ's peace control our hearts. I do not think the person who was upset by my mention in my professed eremitic vows to include canonical obedience fully understood but rather got the meaning and intent confused with canonical approval of hermits by one's specific diocese bishops according to Canon Law 603. ]]

In such an act the subject making their profession becomes a "Hermit of the Diocese of x_________" and they do so not merely because they are a hermit living in that diocese but because they represent the eremitical life in the name of both the local and the universal Church. With private vows --- which, again, do not rise to the level of profession as the Church understands this term --- the hermit involved does not become a "Hermit of the Diocese of x____" and is not bound to canonical obedience despite the fact that she may live eremitical life in that diocese. It is too bad some with private vows feel a need to conflate these with canonical vows. It is always important that those with canonical vows do not embrace a notion of superiority vs inferiority when comparing public profession to private dedication, but at the same time it is crucially important that those who are privately dedicated do not mislead or confuse by misapplying terms like "canonical" when characterizing their own vow of obedience, etc. This is a source of serious confusion and does not serve the Church or the differing expressions of the eremitical life particularly well.