Good question;
Most re-enactment units love the publicity, in order to help in recruitment of their ranks.........other than that, there is little advantage in doing something for the history channel.....

...They do not pay for your ammo/blanks, & fuel in the vehicles. little in the way of paying for travel, etc.......
*** The worst is, if they are invitied to a closed event battle, in order to film it, they are not happy with just being allowed to be in uniform, be in the midst of the battle-field and film.....!....They want re-runs done, and that is just impossible, because it interfers with the tactical action!....So therefore, many units, just decline.
Last year, the history field team wanted to go to our trenches of the Russian Front, out at Marion , Ky....After many phone calls between the unit commanders ,and many others, it was decided to not let them out there. > Primary reason being they would get in the way for the above reasons, and would not be content with just capturing the 'action', and therefore missed shots like below.....

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Beautiful women are like well built machineguns: Some should just be looked at, and left alone, while others were built to get hot.