Hawke's Investigation

I don't think they can be regarded as Red Templars when he was investigating them. They only became a cohesive group after the events at Therinfall. Hawke knew about red lyrium from the idol and what went down with Meredith. It might reasonably be assumed that it was red lyrium that gave her extraordinary powers and ultimately sent her mad. Hawke clearly maintained contact with Varric, so it could have been him who first made Hawke aware of the rumours that some Templars were continuing to use the strange new lyrium. Regardless of how Hawke heard what the Templars were up to, even if Hawke had left Kirkwall it is likely they would be concerned about this. In fact if Hawke was supporting the mages they would likely be even more concerned if Templars were using this new type of lyrium to make themselves even more powerful. So either way, Hawke had a vested interest in looking into it.

Hawke then says that this led them in the direction of the Wardens. I am not quite sure why that should be but may be it was to do with the source of the red lyrium the Templars were using. Clearly it had to be separate from the idol/Meredith's statue, which were under close guard. Since Hawke had originally found the ancient thaig with the aid of Warden maps, it was sensible enough to contact the Wardens to see if they knew of any unusual activity in the Deep Roads.

I have to admit that anyone other than Stroud being Hawke's contact is harder to explain. However, during the battle for Kirkwall against the Qunari, the Wardens do step in briefly to help and whilst their default leader is Stroud, it is also possible for them to be either Alistair, if still in the Wardens, or Loghain (I assume since I never had a world state with him alive). Thus I presume that Hawke would regard the assistance they received from the individual against the Qunari was sufficient to overcome any prejudices they may have had against Loghain because of Ostagar. After all, I presume the word would have got out that Loghain was recruited to the Wardens to atone for their previous crimes and in any case the rule is that becoming a Warden pretty much nullifies anything you had done before. Alistair may have thrown a hissy fit because he sees it as a noble chivalrous order of knights but what Riorden suggested for Loghain was in keeping with the traditions of the Wardens and accepted as valid across Thedas. Duncan was a murderer and a thief before joining the Wardens and Rainer was recruited by the real Blackwall even though he was guilty of the murder of innocents. The Wardens don't care what you have done so long as you have a reasonable degree of skill and are willing to fight darkspawn. Plus the Joining is considered a form of divine judgement. If you survive it, clearly you are worthy of being a Warden. It is as a Warden that Hawke is willing to work with Loghain.

Ah well then, personal gratitude isn't involved but the rest is true. I suppose we have to assume that Hawke contacted Stroud first and it was he who directed them to Loghain. In some ways Loghain being involved makes more sense than either Stroud or Alistair, since the former is a leader of the Wardens in the Freemarches, whilst Alistair is connected with Vigil's Keep (strangely absent from the plot in DAI) but in DAO Loghain was being sent to serve with the Orlesian Wardens so it makes sense that he would fall foul of Clarel in that case and then flee back to Ferelden. Although of course the codex letter from Clarel to Teagan suggests she needed his permission to enter Ferelden, which was curious considering the plot of DAA and whilst she had no jurisdiction there as leader of the Orlesian Wardens, she should have been able to enter without his authority if she had business with Vigil's Keep. During the Blight the chief reason Loghain refused entry to the Orlesian Grey Wardens is that they had a load of Chevaliers with them and clearly he was worried the latter might not return home once the Blight was over (as had been the case in previous Blights).