If you do run your own wire, use a good quality RG 6 cabling and use Snap n Seal fittings (available at Lowe's Depot). I would also go the extra mile and finish the inside outlet with a wall plate. I don't like it when installers cut corners and just pull cabling through the wall/floor and just terminate the end of it.
They will have to install a grey box (similar to a telco demarc) where the cable comes in because NEC now requires that ground blocks installed outdoors must be in a weather resistant housing. When I was living in Iowa, the cableco there installed a weatherproof box for the ground block that was large enough to house 20 ground blocks (although I think splitters now need to be in weatherproof enclosures as well).
My ground block and splitters are in the basement on the ceiling adjacent to the electrical panel.
I would also go the extra mile and finish the inside outlet with a wall plate. I don't like it when installers cut corners and just pull cabling through the wall/floor and just terminate the end of it.
A direct connection to the cable modem (with no intermediate wall plate splice connection) is only a "cut corner" if it is done against your wishes. The OP has already stated that a simple direct connection is exactly what is wanted in this particular case. -- We can never have enough of nature. We need to witness our own limits transgressed, and some life pasturing freely where we never wander.
I just had a new install (internet only) and they did not install a box. They did install a the ground block and ground rod but just bolted it to the siding. They used my RG6 that I had run from the modem and put on their connectors.