From the ATC youtube: the intercom calls in the G/A come from a female and advise speed and altitude need more control. All ATC calls on approach come from her. It would suggest she was PNF. About EIN's refusal: a declaration of a fuel emergency would shake them up and open many doors and runways. Heads would roll if you were still refused for some BS reason. Sometimes it's time to confirm who needs help and priority: usually it's the guy in the air not on the ground. I remember a BA flight into AMS when the wind was strong WSW and gusting. He was given 19L (old days). Firstly he was approaching that runway direct from London, and RW27 was not in use due noise allocation ratios. He asked if the wind was veering as it gusted. Affirmative from ATC. It was a strong nasty day. He asked for RW27. This was refused as not in use. He asked if it was closed as unserviceable or serviceable. Yes it was serviceable. He requested it again. Refused. He then said he refused 19L and said if he had to divert to BRS there would be a report and strong complaint made about AMS ATC and perhaps they would get the bill for the diversion. RW27 was opened. The captain retained and exercised responsibility for the safety of the a/c.
I once was an F/O on a biz-jet. We wanted to land at a remote airfield for our pax. It was a few seconds after official closure, but all facilities were present. ATC said we would have to divert unless an emergency was declared. Guess what happened. Local security inspected the a/c on arrival and we declared fuel load as the reason for emergency. They said we still had fuel in the tanks. We asked how much is enough and how much is too little for this a/c? Silence, and they left with a beer each for the onboard bar. Captain's call, but pax were happy.
Sometimes a bit of push is required to get what you need/want. I agree one is more serious than the other, but.......