That was just Kirk thinking the Iotians didn't know, though. Kirk knows relatively little about things that happened a century before his watch - see "Balance of Terror". If Kirk was mistaken about the history of invisibility tech, he might have been confused about things like subspace radio and transporters, too.
As for Kirk not having formal permission to come aboard the
Enterprise if beaming up using Starfleet HQ transporters, it would have been a trivial matter of phoning the ship first.
Even when the Klingons are boarding her they use the transporter pads.
Umm, the Klingons in ST3 apparently use the actual transporters of the
Enterprise! The sparkle effect is the blue Federation one, not the red Klingon one. Apparently, Kruge's ship was shot to pieces at the time, and only managed to repair her own transporters some time later, leaving Kruge at the mercy of the Starfleet transporter operator - which wasn't a problem, because that operator in turn was at the mercy of Kruge's nicely functioning disruptors and torpedoes.
FWIW, we know that a non-Klingon pad can receive a Klingon signal, too - this happens with the Cardassian unit at DS9 Ops in "Dramatis Personae". This isn't a case of the Klingons beaming onto an inert Cardassian pad, either, as the Klingon transporter had exploded several seconds before the materialization attempt with the red sparkling took place... (The attempt failed, but the signal was not lost, and the heroes managed to materialize it from an amber Cardassian sparkle moments later!)
So we have three distinct modes for pad-to-pad: 1) pad A sends people to inert pad B, 2) pad A sends a signal that pad B actively materializes, and 3) pad B grabs people from inert pad A. And from that DS9 ep, we know that we cannot predict the sparkle color in case 2: it can be typical to pad A or to pad B.
In most episodes, it would seem that the pad operated by our heroes is the active one, and it is difficult to demonstrate it wouldn't be the
only active one. But ST:TMP is a confusing case where two pads seem to be active simultaneously or near-simultaneously - so either some variant of case 2 above, or a flip-flop between cases 1 and 3.
The dialogue there is beyond ambiguous, of course, but from that DS9 episode we know that a signal can be juggled inside a system formed by two transporters, including one that is badly broken (or vaporized!), until materialized at one end or lost forever. TNG "Realm of Fear" adds the option of the pattern remaining in limbo inside a buffer adjoining one of the transporters, and various other eps suggest select elements of the pattern may remain behind while others are either lost or materialized or unconventionally stored (as pure data; as energy-based lifeforms; etc.). We could easily argue that the
Enterprise is doing all the beaming in ST:TMP, until their transporter hiccups and Rand says "Override!" at which point Starfleet HQ activates their own pad for the very first time and tries to receive the phased matter package that's loose in the system.
Timo Saloniemi