I think that on the trade screen the strings are due more to diplomacy ability than military power, unless the AI is threatening you. I only glanced at that code briefly before replying, but I'll look into it a bit more later.
The fields and their values in english.str that indicate Military strength are involved in threats are "Human_ThreatDumb", "BlackmailRejectStronger_X", "ThreatResponseHumanStrongEco", and "TributeDemand_Default".
In general, what I said was correct. The Threat/Blackmail strings are used if there is only an offer on one side, ie either you or the alien is asking for something for nothing.
The calculation used to determine who is stronger on the diplomacy screen for threat strings is the military might + economic might. So even if the AI has a weaker military, if they have a stronger economy, they could still come out as stronger. If their economy is in the hole and you're still getting that message, there could be something in the economic might calculations that is screwy.
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