It is true of born-again believers who are truly, genuinely, and thoroughly converted (according to the SOP definition) and while they are actively, aggressively abiding in Jesus and partaking of the divine nature. I suspect Peter experienced this state and status around the time of Pentecost. Unfortunately, when Peter dissembled, he wasn't at that point and during that time abiding in Jesus and partaking of the divine nature.

What kind of authority do you think this text "invests upon the Church?"

The passages I posted earlier on this thread indicate Jesus commissioned the Church with administrative authority. It is all encompassing dealing with doctrine, baptism, membership, discipline, and business.

What have you discovered about it?

Without sanctified leadership there is choas. Everyone pulling in an opposite direction. So yes, the church needs to have administrative authority.

That said -- I would caution everyone NOT to put absolute confidence in the decisions of the leadership.
They can make mistakes.

One example is what's going on in Samoa.
The Islands returned to their position west of the dateline, lining up with australia and New Zealand.
The church leadership in that territory decided they would reject the move across the dateline when it comes to the Sabbath and continue to operate on the east side of the dateline to determine what day to worship upon, but on the west side for the rest of the week.

So now they worship on Sunday. On Saturday they do whatever.
Their week looks like this:
Sunday (Sabbath)
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday (ordinary work day == preparation day)

There is a growing group who can't agree.
They are being harrassed as "Saturday worshippers" and in defiance against "CHURCH AUTHORITY".

Should they simply bow and say "whatever the church decides we will do?"

Or are they correct in witnessing that the seventh day is Saturday, the day between Friday and Sunday?

They have appealed to the highest level of the church and are praying

They should abide by the Samoan government decision and observe Sabbath on the seventh-day.

I realize that's not what you said, but imagine if the Islands were moved out of their place. Would that make a difference? I would think not, that they would go with what their leaders tell them to think.