They did.
From the report "JUSTITSMINISTERIETS FORSKNINGSKONTOR AUGUST 2011
MENNESKERS SEKSUELLE OMGANG MED DYR En undersøgelse af dyrlægers kendskab hertil" (PDF):
Table 1 shows how many of the veterinarians during their time as practicing veterinarians have suspected that animals they have examined have been subjected to sexual intercourse with a human. It appears that 80 veterinarians have experienced this, which corresponds to 17 per cent of the respondents.
(my translation, p1)
For context and in response to OP stating that such a 'number seems rather high': it is; and needs to be taken with some salt.
First, it does not mean that of all animals in Denmark seen by a veterinarian in one year 17% would qualify for the stated category.
Only that of all vets asked 17% responded with 'yes, I've seen such cases'.
The samples were also quite small and the survey methods – hm – not overly robust, and stretching over quite a long time.
Based on further translating the text of the study:
A previous study from 2006 done by the Danish Council for Veterinary Ethics was similar: they approached veterinarians in Denmark via the Danish Veterinary Association's joint email list regarding human sexual intercourse with animals. The survey resulted in 114 responses from current or former practicing veterinarians with experience based back to the 1970s. These veterinarians report a total of 17 cases where, through their work, they themselves have suspected human sexual intercourse with animals and / or had the suspicion confirmed. In addition, the study mentions cases that the veterinarians are not aware of, but have only heard of others. It should be noted that the study is not based on a representative sample of veterinarians, and that the purpose of the study was not to map the extent of human sexual contact with animals, but rather to gain insight into veterinarians' relevant experiences in the field.
Apart from knowing the characteristics of the sample, it is therefore quite instructive to know the actual question asked in that survey:
During your work as a veterinarian, have you ever suspected that a human has had sexual intercourse with an animal that you have treated or consulted?
(From p8, appendix, "Spørgeskemaet til dyrlægerne" ("Questionnaire for veterinarians"))
And even with all those caveats, it seems useful, to avoid being misled, to focus on the summary of the report:
The study has shown that a relatively small proportion of the country's veterinarians through their work have suspected that animals they have treated have been the subject of sexual intercourse with humans 17% of them say they have had such a suspicion.
This must be seen in the context of the fact that veterinarians generally have many years of experience, as they have practiced as veterinarians for an average of 23 years.
The study further shows that less than half of these veterinarians have had their suspicions confirmed, as only 7 per cent. of all veterinarians report a confirmed suspicion. In about two thirds of the cases where the suspicion is confirmed, it is estimated that the animals have suffered harm. This involves damage to the genitals and rectum, and in three cases it is reported that the animal has had to be killed as a result.
The study also sheds light on the annual incidence of suspicions of human sexual intercourse with animals and the number of confirmed suspicions, respectively. With the uncertainty that may exist in a precise timing of serious cases, the study suggests that there will be 5-12 suspicions annually and that less than half of these will be confirmed. That is, the suspicion can be expected to be confirmed in 3-5 cases annually. Not in all these cases will the animal suffer any harm.
It should be emphasized that this study is not able to shed light on the extent of human sexual intercourse with animals, but it must be expected that it may give an impression of the extent of cases where animals have suffered more serious harm as a result of human sexual intercourse with them.
So at first glance or on a fast reading, the 17% sounds like a surprisingly high number. But all it says is that such behaviour really does exist and is 'common enough' for veterinarians to have experienced a few cases when they had such a suspicion. For each positive respondent between 1 and 5 times altogether over an entire career, averaging 23 years.
The actual prevalence of such behaviour in the general population is not inferable from this number "17%" and from the whole report it seems rather quite low overall.
