This is complex because there are several issues to consider in this situation.
There are several issues to discuss with herpes blood tests and I do not completely agree with the statements by your doctor, so will quote studies in the literature where I disagree, because you obviously do not know me.
First, is that there is a chance that the test is wrong, i.e., a false positive. When measuring antibodies, they actually generate a numeric number reflecting the activity of the antibodies. In anyone, there is some background cross-reactivity with the antibody, so they will compare the individuals numeric value to the maximum possible background value and calculate an index. An index of 1.0 means that the individual is at the maximal background level. An index that is <0.9 is considered negative, while an index >1.1 is considered positive, and an index between 0.9 and 1.1 is considered inconclusive. However, even with a positive result, it is possible that the result is a false positive. The test is very sensitive, so can generate a fair amount of false positives, and the likelihood of false positives is greater if the result is only mildly positive. For example, in this study, if you look at Figure 1, only 15% of people with an index between 1.1 and 1.5 are truly positive when a more accurate test is done. It is only with an index that is >3.5 that there is a >90% likelihood that it is a true positive. In someone having typical symptoms, there is less reason to think that there could be a false positive, but in someone with no symptoms, the first step when there is a positive HSV2 IgG test is a review of the index and consideration whether a second more accurate test should be done, such as a Western Blot test.
If there is confirmation that you are truly positive, then the meaning of the positive result is the next issue.
Herpes Simplex Virus type 2, or HSV2, will usually cause genital herpes, while HSV1 will usually cause oral herpes. However, there is some crossover, with HSV2 causing oral herpes or HSV1 causing genital herpes. A blood test cannot determine the site of infection. The antibodies that are formed from the common HSV2 genital infection are identical to the antibodies that are formed from the uncommon HSV2 oral infection. If the oral cold sores first started as a child, it is even more likely that it is HSV1, but if the cold sores developed in adulthood, then while still uncommon, there is a slightly greater chance that it is HSV2 that caused the oral cold sores. The vast majority that have a true positive HSV2 IgG test have a genital infection, but if there are no symptoms, it cannot be definitely stated from a blood test. If there is a positive HSV1 IgG, then that would support that the oral cold sores were from HSV1, while if there is a negative HSV1 IgG, then that would raise the likelihood that your oral cold sores were caused by HSV2. However, the only way to prove whether someone is having oral HSV2 or genital HSV1 is to perform a culture of a sore from the respective area. This is frequently impractical, so doctors will frequently assume that a positive HSV2 IgG indicates a prior genital infection, and they will be correct the vast majority of the time, but there will be exceptions.
The next issue is whether someone with a true positive blood test has any viral shedding. In the typical genital herpes infection, there are occasional sores and large amounts of viral shedding when there are sores. In between the episodes of sores, there is usually no viral shedding, but there are some days of shedding of the virus on days when there are no sores, called asymptomatic shedding. In someone with no symptoms and a positive blood test, the question becomes whether there is any shedding of the virus. There is a common misconception that someone with no symptoms is not infectious, but a study from a few years ago showed that people with no history of infection in whom there was a positive test frequently had viral shedding when genital swabs were tested for the virus - see Figure 1 in http://jama.jamanetwork.com/article.aspx?articleid=896698. Even in the worst case, there is no shedding on most days, as is also true in someone with a symptomatic infection, but shedding could be detected. There were also many patients in whom shedding was not detected, but since the study was only for a limited period of time, it is not sufficient to prove that these people never have shedding. So, from this study, it can be said that some people with no symptoms and a positive blood test can have asymptomatic shedding, although there are also some that may not.
It is also worth noting, as I tell everyone that gets infected with genital herpes, that the greatest impact of a genital herpes infection is the psychologic and social impact of the infection, since it cannot be cured. The physical consequences of this infection is minor, in the same way that the physical consequences of an oral herpes infection is minor. But the psychologic and social impact is much greater.
So, there is a chance that you are not truly positive, and the index should be requested from the lab. But if you are truly positive, there is a chance that you are having asymptomatic shedding, so it cannot be said that you cannot pas it to your partner.
If I can provide any clarification, please let me know.