Ok, thank you for the direct example. This is a a pretty simple case compared to many others (IAP chart below).
If the aircraft is cleared for a straight in approach (i.e., bypassing the Hold-in-Lieu) from CIRIX, clearing someone to join the approach at 4,000 is legal.
You fully meet the three requirements quoted above.
More practically speaking though, the instant they hit CIRIX inbound, their IAP MEA is 3,300 to REYOS, lower than the 4,000 they are at when they join the IAP. Clean.
If they aren't in a position to do the straight in approach, then they need to be at or above 4,500.
The published holding pattern doesn't exist below 4,500, that is the minimum holding altitude by definition. If you clear someone for approach when below 4,500 from a position where they need to execute that course reversal, they aren't on a published segment of the approach once they cross CIRIX outbound per the clarification of Note 3, which in turn creates a violation of 4.8.1.b.2. Basically, they're in no man's land.
Even if you argue "well, he stays at 4,000 feet until he hits CIRIX, and that's above my MIA, so it's ok," well...
TERPS had a reason to designate that hold minimum altitude at 4,500 instead of at your MIA of 4,000. According to the Holding Fix Record for CIRIX, there is an Adverse Assumption Obstacle controlling the minimum altitude (in fact, the minimum altitude was raised from 4,000 to 4,500 in May 2012).
I get this is down in the weeds and are things neither the controller nor the pilot are expected to know, think, or worry about, just the number on the plate... simply stated, I think it's harder if not impossible to establish good standing to clear someone to fly the holding pattern as published below the minimum holding pattern altitude.
In short...
If the aircraft can meet the 90 degree rule at CIRIX, they can be cleared straight in at 4,000. If not, they need to be at 4,500 and allowed to execute the Hold-In-Lieu.
PS - Addressing the TAA, I'd say this doesn't restrict you in terms of the 4,000 for a straight in as discussed, it just serves to reduce your phraseology a little by reducing phraseology you need to state when clearing someone for approach direct CIRIX, and they're AOA 4,500 and within 30 NM.
If anyone has counter-arguments, I'm willing to listen, not trying to say I have the final word, but I think I've got a tight case.