Per New Jersey Law spanking is not illegal as long as it is not used in excess. The issue is more likely the belt then the spanking. While parents are allowed to spank the parent also must use this in moderation. A belt could be deemed excessive so this may be something you want to reconsider in your punishment regimen. There will always be someone who feels spanking is abuse, but the law is quite clear that it is not.
As far as being concerned, if the counselor believed it was a issue of abuse the child would have been removed from the home. Basically when claims of abuse are made the counselor is obligated to report this to child protecting services. What will happen is a worker will talk with the child and with the parents and do a quick home study. There are two ways of handling this, one right one wrong. If you are hostile, aggravated and refusing to cooperate this can drag out for a while. If you are polite and allow them to do their job most often then not the case is settled quickly if there is no abuse.
The fact is they have a job to do, and that is to protect children. They understand children and how they operate well lol. Every child at some point or another try to manipulate people. They will speak with the child and with you and ask how you punish the children. Be honest and try not to be defensive. Let them know you know the difference between disincline and abuse. As far as can they interrogate the child, the answer is yes. The law provides for them to speak with the child at the school or at home without the parent present. This is standard procedure.
Here is the law on spanking in New Jersey:
Cruelty to a child includes inflicting unnecessarily severe corporal punishment upon a child. Sec. 9:6-1.[Ci.] "Abuse" includes a parent, guardian, or other person with control or custody inflicting excessive corporal punishment (which must be excessive to the point that the child's physical, mental, or emotional condition has been impaired or is in imminent danger of becoming impaired as a result). Sec. 9:6-8.9.[Ci.] Person with responsibility for care, supervision, discipline, or safety of another may use force against them if for the purpose of and to the extent necessary to further the responsibility. Sec. 2C:3-8.[Cr.] Justification is not available if the person recklessly or negligently injures or creates a risk of injury. Sec. 2C: 3-9.[Cr.]
I wish you and your family the best,