The cost of a province is only affected by
- the distance from your city
- your advanced scouts tech and
- how many provinces you have scouted (minor)
That cost determines how many enemy units you will face. Once you start a scout this can never change for that province.
The color or difficulty of a province is based only on how many units you bring vs enemy units.
How many units you bring is affected only by your squad size, so increasing this will change the color and difficulty rating even after a province has been scouted.
So, while support is correct in that researching those techs won't change the cost/enemy side of the equation they will change your side and make battles/ratings easier.
Note: other military techs like unit upgrades will certainly help you win battles as will certain buildings in your city, but those are
not reflected in the color/difficulty rating of a province.