Dillard, 40, who asked the council during public comments to stop making cuts to public safety, said she wants enough officers to take reports at all accidents, not just special cases.
"If I were to be in an accident, I would not have direct access to the chief's number," she said.
Small said it isn't unusual for him to respond when people call him directly, adding that he would help anyone who asked.
"Some might say, 'Gee, people are calling the chief to get service,' and I say, 'So what?'" Small said. "'I get to be open and accessible when people who know me have a problem.'"
Small said that while the policy serves as a guideline, the dispatchers do, on many occasions, send officers to non-injury accidents.
"I know we have a policy that says we don't respond, but there are a lot of times when we do send somebody," he said. "The dispatcher has the discretion."
He blamed the dust-up on politics.
"Personally, I think somebody is using this to embarrass Devin," Small said, adding that Dwyer is a friend from church. "And I just don't think it's appropriate to do that."
Dwyer, in an interview, asserted that Dillard is a "stooge" of the police union.
"They are the ones [who] are saying that's a special treatment because they feel I'm going to continue to make cuts," he said. "Am I gonna pay $200,000 an officer? No. They're overpaid and under-worked."
"He [Dwyer] doesn't even know me," Dillard countered. "How would he know that?"
Dillard denied being influenced by the police union and said she found out about the incident when Small mentioned that a friend of his called him for service on a non-injury collision during the Sept. 17 study session.
Small said he mentioned the incident during the session to illustrate services that were eliminated by budget reductions.
Dillard said she has some police officer friends, but none asked her to inquire about the accident or speak out.