The Census of Agriculture's 2014 Organic Survey, which includes data from all certified organic farms in the United States at the time, has some data on the use of fertilizer by organic farms.
Table 20 contains information about production expenses for organic farms, one expense being "Fertilizer, lime, and soil conditioners". Of 14093 organic farms in 2014, 9298 (66%) reported having expenses for fertilizer, lime, or soil conditioners.
Note that not all organic fertilizers are animal matter. The list of organic fertilizers allowed by law is:
Fertilizers that are specifically banned are:
- Any fertilizer or composted plant and animal material that contains a synthetic substance not included on the National List of synthetic substances allowed for use in organic crop production
- Sewage sludge
Additionally, Table 21 in the survey provides the information that 9409 farms (67%) used green or animal manure for crop production. Green "manure" is plant matter, not animal.
Unfortunately, neither of these numbers directly represent the use of animal matter by farms, but they do give us a rough upper bound of about 2⁄3.
The full 2012 Census of Agriculture Report gives us information about conventional farms. According to the report, there were 2109303 farms in 2012. This number is large enough that it is pretty insignificant that organic farms are included in it (less than 1% of farms were certified organic in 2014).
Table 49 gives us the numbers corresponding to those we found for organic farms. Of all the farms in 2012, 1011896 (48%) had fertilizer, lime, or soil conditioner expenses, and 275420 (13%) used manure (or green "manure").
The numbers published by the Census of Agriculture suggest, but do not prove, that a higher proportion of organic farms use animal matter than conventional farms. This would not necessarily imply that organic farms use more animal matter per yeild; it may or may not be that organic farms use less fertilizer overall.
Of note, is that a similar number of organic farms reported using manure and having fertilizer, lime, and soil conditioning expenses, but many less conventional farms reported using manure than having fertilizer, lime, and soil conditioner expenses. This suggest that most fertilizer used by organic farms is manure, but it is possible that this is a coincidence.
Overall, it is probably true that a higher proportion of organic farms use animal matter than conventional farms. It is not, however, reasonable to assume that most product labeled organic were grown using animal matter, since only up to 67% of organic farms use animal manure.