How do Killstreaks affect Mediguns?

Solution 1:

Yep, you've got it. When a medic gets an assist while using a medigun, that assist will be be counted as a kill for the purposes of the killstreak counter. Mediguns work exactly the same as normal killstreak weapons which gain effects upon hitting kill threshholds, except that the counter is increased by getting assists.

Here's a video showing the medic getting a killstreak while his heal target kills enemies. Look for the streak counter in the bottom-left. When the medic gets to 10 assists, he gets the same kind of server-wide message anyone else with a ten killstreak would get.