I think it's a bit much to expect to expect someone to be able to guarantee perfect conditions given the ocean is a constantly changing environment. I've spent a lot of years around the water and I never met anyone that could predict conditions to the precision you're suggesting.
Agree, to a point. However, OP said capt. stated "no moon, slack tide, no current". Sounds like the captain either hadn't checked the tide charts, or dropped them off late. The "noticeable tug that started to increase" tells me they missed the slack; they dropped in and felt current which picked up. If you're diving on the slack, typically you should feel some current in one direction, which decreases to nothing, then switches and runs the other way & picks up.
I have no idea where the OP was diving (Desitn? Is that Destin, FL?), or what kind of currents they have there. I've dove plenty in the Georgia Strait, where we can get some wicked tides. Slack dives are fun; rather than starting your dive into the current, you drift WITH the current until slack, then have a brief period of calm, then drift BACK with the current to your entry point. It can be almost like drift diving, but the boat can wait for you to come back where they dropped you off.

If you miss the slack, though, and don't notice that the current is picking up instead of slowing.... well, you can go a long, long way. All that said... I completely agree. Trust that the captain knows his waters and is on the mark, but verify too.