ByzCath:
I do not believe this is true. I have attended Masses that were not open to the public.
One was a private Mass of a prayer group. Only those invited to the event where at the Mass.
The others were at religious houses that is not open to the public.
First let me take the opportunity to offer congratulations and prayer to you upon your acceptance!
Even though you had these experiences, as many of us have, this is not the case in the law of the Latin Church.
While there is not an obligation to publicize the time and place of a Mass celebrated in the presence of a private group, or an obligation to “invite” others, if an uninvited Catholic had shown up to the prayer group in a church, the obligation to admit that person would normally oblige on the basis of the canons I cited previously.
Religious houses usually have oratories, properly speaking, and access of members of the Christian faithful apart from the members of the house is not presumed by the law. The right to have an oratory attached to an erected religious house is treated in canon 608, “each house is to have at least an oratory in which the Eucharist is celebrated and reserved so that it truly is the center of the community.”
Canon 1223 describes an oratory as “a place designated by permission of the ordinary for divine worship for the benefit of some community or assembly of the faithful who gather there; other members of the faithful may also have access to it with the consent of the competent superior.”
Canon 931 also mentions, in addition to an oratory, that a church might be attached to the house of a religious institute or society of apostolic life. In this case, canon 1214 cited below would presume the right of access.
Private individuals may have chapels under canon 1226: “The term private chapel signifies a place designated for divine worship for the advantage of one or several physical persons with the permission of the local ordinary.” Public access is not be presumed for divine worship in such a private chapel.
God bless.