...... that here of all places there seems an inability to understand the threat the Royal Navy faced in 1940.

The large but mostly WW1-built RN battlefleet faced a small number of modern and greatly superior German capital ships.
As the Bismarck action showed, it would require a whole fleet of older RN capital ships to take out each modern German battleship. The RN numbers were just sufficient to do that, but only if great care were taken. The loss of the Hood was a savage reminder how costly any misjudgement of relative vulnerability would be when sending naval units after the German battleships.

Now the RN faced the possibilty, no matter how remote, units of the French Navy could be used against them and destroy that delicate balance. In that situation no one can afford the luxuries of trust or pieces of paper. The matter had to be put beyond doubt.

The French refused to co-operate. In my view Churchill had no choice. This was a War-Losing issue. Most commanders in this situation would have done the same.