It's an over-generalization, to be sure, and there are a few problems with the premise. It's also quite hard to give a quantifiable answer on 'peace,' as that's a relative term depending on a culture/people's understanding of the term.

Problems:

• Limited indigenous source material: most of our existing source material on pre-colonial Africa comes from outside sources, thus there's the issue of observation bias. This would be less problematic if it weren't for racial and cultural boundaries leading these outsiders to produce potentially-false conclusions. Many records of pre-colonial Africa are produced via archaeological and anthropological work, each of which comes with its own set of observational problems. In short, it's extremely hard to pin down a singular narrative of pre-colonial African history without accepting that much of the story we know is the result of third-party interpretation. (This is not to say that primary sources recorded within one's culture are uniquely objective, but rather that the subjective lens becomes more and more skewed as one leaves a cultural frame of reference.)
• The nationalist issue: during decolonization, it was fairly common for anti-imperial nationalists to call upon national history as a means of unity. This is unsurprising, but it did come with some problems. Often times, these leaders would downplay past strife within their culture to emphasize the importance of national unity in the face of western imperialism. These statements have permeated popular conceptions of the past with regards to post-colonial development. I imagine the statement being made by your professor stems from this misconception. Here's an [example] (https://books.google.com/books?id=fEABxEbLmg4C&pg=PA37&lpg=PA37&dq=%22I+hold+this+to+be+a+mistake.+The+English+have+taught+us+that+we+were+not+one+nation+before+and+that+it+will+require+centuries+before+we+become+one+nation.+This+is+without+foundation.+We+were+one+nation+before+they+came+to+India.+One+thought+inspired+us.+Our+mode+of+life+was+the+same.+It+was+because+we+were+one+nation+that+they+were+able+to+establish+one+kingdom.+Subsequently+they+divided+us.%22&source=bl&ots=8cS6Kyp3xK&sig=hb1fNYHt7n1TW8BuYe-dQ-i0CCg&hl=en&sa=X&ved=0ahUKEwjY25-hz-HKAhVIvRQKHbmmB0sQ6AEIKDAC#v=onepage&q=%22I%20hold%20this%20to%20be%20a%20mistake.%20The%20English%20have%20taught%20us%20that%20we%20were%20not%20one%20nation%20before%20and%20that%20it%20will%20require%20centuries%20before%20we%20become%20one%20nation.%20This%20is%20without%20foundation.%20We%20were%20one%20nation%20before%20they%20came%20to%20India.%20One%20thought%20inspired%20us.%20Our%20mode%20of%20life%20was%20the%20same.%20It%20was%20because%20we%20were%20one%20nation%20that%20they%20were%20able%20to%20establish%20one%20kingdom.%20Subsequently%20they%20divided%20us.%22&f=false) by Gandhi (see p. 37): "I hold this to be a mistake. The English have taught us that we were not one nation before and that it will require centuries before we become one nation. This is without foundation. We were one nation before they came to India. One thought inspired us. Our mode of life was the same. It was because we were one nation that they were able to establish one kingdom. Subsequently they divided us." This narrative of Indian history is unfounded, and is quite problematic in the context of Indian nationalism.
• Relative terminology: As noted above, the terms 'war' and 'peace' are diplomatic, and are largely treated as a binary opposites. That's not necessarily the case, especially when discussing the history of Early Modern or pre-Early Modern periods. More information would be needed in order to determine what is meant by the term 'relatively peaceful.'

I'm not comfortable offering a definitive answer to the question, and I warn against attempts to do so.

Sources:

• Gandhi's Hind Swaraj (referenced above)
• Frederick Cooper, Decolonization and African Society: The Labor Question in French and British Africa (Cambridge, 1996)
• Rupert Emerson, From Empire to Nation: The Rise of Self-Assertion of Asian and African Peoples (Cambridge, 1962)