Another explanation for the use of toward over at is that in the context given English speakers have heard "toward" used since their childhood. Usage dominates the reason for one preposition over another in the English language.
I would have to feel that it was the writer's taste to employ to instead of towards or at. Don't be confused. Just try to understand that with English prepositions there is not always an absolute rule which favors one preposition over another. An author can use his own tastes in many cases such as toward, to and at.
An example of what Harry is talking about is the use of prepositions with the word "different." Is A different from/to/than B? Many AE speakers would choose different from, while many BE speakers would say different to. I've also heard different than used in both AE and BE.
You could always use Google or, better yet, search specific corpora (WR link listing several) for the specific phrasing. You can analyze the various examples offered and perhaps roughly assess which phrasings are more idiomatic or at least more popular in more formal writing.