Big Blue and his Combat Boots say they have the Legal Right to Board your Vessel! They are going to do the Deck Scuff Dance on your baby! Safety Check or Legal Harassment? Do you have rights?

Alright - what happened??
I believe they can ASK to board, and you can refuse.
If they have reasonable cause, or, if you cannot produce the things they ask for (safety gear, documents...) they can legally board.
I'm not sure on this, just guessing.
Let the experts chime in.

US CODE 14 USC 89

(a) The Coast Guard may make inquiries, examinations, inspections, searches, seizures, and arrests upon the high seas and waters over which the United States has jurisdiction, for the prevention, detection, and suppression of violations of laws of the United States. For such purposes, commissioned, warrant, and petty officers may at any time go on board of any vessel subject to the jurisdiction, or to the operation of any law, of the United States, address inquiries to those on board, examine the ship’s documents and papers, and examine, inspect, and search the vessel and use all necessary force to compel compliance. When from such inquiries, examination, inspection, or search it appears that a breach of the laws of the United States rendering a person liable to arrest is being, or has been committed, by any person, such person shall be arrested or, if escaping to shore, shall be immediately pursued and arrested on shore, or other lawful and appropriate action shall be taken; or, if it shall appear that a breach of the laws of the United States has been committed so as to render such vessel, or the merchandise, or any part thereof, on board of, or brought into the United States by, such vessel, liable to forfeiture, or so as to render such vessel liable to a fine or penalty and if necessary to secure such fine or penalty, such vessel or such merchandise, or both, shall be seized.
(b) The officers of the Coast Guard insofar as they are engaged, pursuant to the authority contained in this section, in enforcing any law of the United States shall:
(1) be deemed to be acting as agents of the particular executive department or independent establishment charged with the administration of the particular law; and
(2) be subject to all the rules and regulations promulgated by such department or independent establishment with respect to the enforcement of that law.
(c) The provisions of this section are in addition to any powers conferred by law upon such officers, and not in limitation of any powers conferred by law upon such officers, or any other officers of the United States.

I take it they were local water cops or state?

It didn't take long for the experts to show up.

you should always play nice with the CG............they really are here to protect us boaters..........

last yr I had two CG boats with guns on the front of each approach me. The guys were very profesional and asked to board. He ask me if it was ok to step on my back seat and I placed towels down for him to step on. He had no proplem letting my protect my ride.
He and his buddies seemed all about performance boats

I had a similar experience and as they pulled alongside in a RIB? the ones with the hard plastic PEBBLE FINISH sides (not kind to paint), I asked if I could move to put my fenders out...
The one dude ready to secure a line to my stern cleat said "the sides of this wont scratch your boat"

I said politely "I am 100% legal and in order, could you accomodate me?"

they did. Including stepping on the towels and being generally respectful. The one checking my gear and papers got the short end...
I know where the other two's eyes behind the aviators were the ENTIRE time.

I am quite confident the only reason I got stopped and boarded in the first place is because there was NO traffic (late season, mid week on the ST Lawrence, and had a smokin' blonde with me...
I am in a beautiful 353, within 3-4 miles of my slip and these guys had seen me a zillion times both in that stretch of river and in fact, going in and out of my slip when they camp out out front.

Was the halting and boarding pure BS?
absolutely...
but what are 'ya gonne do?

My only problem with the Coast Guards (plural as in various countries) is when their go fast boats don't go fast enough.

Local sheriff lives fifteen houses from me, sees my boat go out every time I take it out. One day he pulls me over cause he said my numbers were not readable. These are the same numers that came on the boat 14 years ago, still in great shape. It was rough when he wanted me to tie up with him, I replied it was too rough, if he wants to board the boat, he was welcome to walk over any time and I left. He hasn't bugged me since. It was total BS.