They both sound fine to me, but I admit that the ‘aim to do’ sounded slightly less formal than the ‘aim at doing’, and I suspect that that was the feeling of your author.
However, I just went looking for more information on the internet, and came up with these interesting comments on another forum:
1– [i]According to my Canadian Oxford, ‘aim’ can either be followed by ‘at’ + a verbal noun (gerund, ‘-ing’) or by ‘to’ + the base form of the verb (infinitive). Both these forms mean ‘to intend’ or ‘to try’.
‘The policy was aimed at providing affordable housing.’
Human beings and organizations can aim to do things.’
'Slogan for a service provider: “We aim to please.” ’
‘The corporation aimed to increase their market share by 10%.’
2– [i]If the goal of the phrase is to highlight what the subject intends to accomplish, as in “The company aims to garner USD for its expansion plans”, then “aim to” is used. Here, the company’s objectives are being highlighted, and the actual objective is not as significant.
If the goal of the phrase is to highlight the object intended to be accomplished, as in “Harvard announces a major new initiative aimed at encouraging talented students”, then “aimed at” is used. Here, the fact that Harvard is announcing the initiative is not as important as the fact that the iniitiative is destined for a certain purpose.
3– [i]When I studied for my Masters in Translation at Westminster U, we studied the concept of idiolect, i.e. some constructs might “sound wrong” or sound “less correct” to each individual than a given alternative. The reason put forward is that each individual has built up a glossary of what he or she has been more frequently exposed to over a lifetime, depending on where his or her parents came from, what he or she read, where he or she lived. This, as can be imagined, generates a mix-and-match type collection of turns of phrase etc that are unique to the individual.
Thus, speaking for myself, when I read the phrase, “the report was aimed at providing” it sounds totally incorrect. I would even have said “grammatically” incorrect.
Also, for me “aim + at” is an Americanism. I wasn’t exposed to it until I starting watching American TV and cinema, as I am a Brit.[/i]