As I say, I'm giving this theory a significant level of suspicion, but it would explain some aspects, although more from the Mauryan side of thinmgs, as opposed to the baktrians. Before Ashoka came to power, he was sent to deal with some rebelling greeks in the north west of his kingdom, and if he was known as a friend of the greeks, that would explain why he didn't need to use any force to stop the rebellion.
seluceaus I, I believe had a 'marriage agreement' or something (It was mentioned in a wikipedia article, so I'll need to double check the date) with the mauryans, so this could, in theory, be Ashoka's mother. It is far-fetched, but it would, to ean extent, explain why the early GBK is shrouided in such mystery.