I do certainly believe that a person can become deviant even if they are exposed to positive influences and even if they have a good support system. There are two reasons why I would say this.
First, some of what we become comes from “nurture” but some of it comes from “nature.” In other words, there are people who are simply born with more of a propensity to do bad things. This propensity can overcome the good influences to which they are exposed. It can be too strong for their support network to overcome. An example of this would be the fact that some people are predisposed to become alcoholic. The excessive and inappropriate drinking that comes along with alcoholism is certainly deviant behavior.
Second, since we are all different, it is very hard to know what “positive” influences are. If a certain style of parenting works for one child but does not work for another, do we say that only one of them got “positive” influences? The point is that something that appears to be a positive influence may actually end up being a negative influence for some people due to their own personalities.
For these reasons, people can be deviant even if they are exposed to positive influences and even if they have a good support group.