Aaron, please move this Q to Products as your next step ("Central" is for non-product-specific marketing topics).
Like Darrell said, you should define what you mean by "the" downloaded asset, since (we hope) a lead will have multiple assets over time.
If you mean the downloaded asset associated with a specific Filled Out Form event, the Activity API has always allowed access to this, provided the asset exists as a field in the form data. (The Forms API allows access to the form descriptor including the hard-coded, form-level Thank You assets, but this is not a reliable source, since there are many other ways to choose a Thank You asset. Plus the descriptor can change over time and no longer reflect what the lead downloaded.)
I don't totally agree with Darrell about using a UTM parameter to transport the asset URL into the form's payload. On a Marketo-hosted LP, you can use a {{my.token}} or variable for the asset URL, so you don't have to always remember to source-tag URLs. Plus, adding a filename to all source URLs can make them look kind of messy IMO, and you someone might hit your LP without UTMs (but should still have the downloadable asset linked to the form fillout).
There are also alternate ways to ensure the URL is queryable that don't involve adding a field to the form. For example, if you use an interstitial Thank You page, you'll log a Clicked Link on a download link and the Thank You URL will also be in the Activity History, so you can see that they downloaded asset Y as a result of form X. Similarly, if you use a redirector page, you'll log a Visited Web Page that contains the interesting data.