The quoted sentence places no restriction on its benefit, and says nothing about initiation. It should apply as of character creation. Following your interpretation, a mystic adept with magician's way would have access to the metamagics immediately, and should use initiation for other purposes.
However, "free use of all regular metamagics" is a very powerful feature that people would talk about in online discussion forums. They don't. It's also problematic from a game balance perspective. Should a character instantly become more capable whenever you buy a splatbook?
Therefore, logic indicates that the RAW phrase "have access to" means RAI "are allowed to purchase". When the sentence is viewed as a redundant restriction on physical adepts, the rules are consistent, although worded poorly.
Reading the section on Ways more closely, I note two things:
- "Because they [...] do not receive a bonus besides the discount on Power Point cost, followers of this Way are able to choose any power they want for the discount." The only quantitative benefit of Magician's Way is the discount, gaining up to PP=(Magic/4) for 20 karma.
- In general, the Ways suck. Beast's Way is marginally worthwhile due to the mentor spirit, and maybe Athlete's Way if you have 3 IPAs to get max discount, but the rest are karma-squandering traps. Your interpretation pushes Magician's Way way beyond the others, to be a mandatory Mystic Adept tax.
p.s. An alternate interpretation of the sentence is that Magician's Way adepts are allowed to poach metamagics from the various Schools without having to be a member (i.e. if you enforce "These metamagics are only available to those who initiate into this school of magic" from p.139).