This is obviously wrong. The use of dual licensing and the ability to provide superior service for open source are unrelated forms of competitive advantage, and without further circumstances, a business should exploit both advantages. Let me explain.
Dual (or multiple) licensing is a strategy, in which a company develops software, releases it under an aggressively reciprocal (“viral”) license like the AGPLv3 and then offers commercial customers who don’t like the open source license the option to acquire a proprietary license for the software. This is a positional advantage of the vendor, because it is the only company that can apply this strategy (courtesy of being the copyright holder). While I mix things up a bit, it is closely related to what’s been called the open core model or single vendor open source. To maintain this positional advantage, vendors need to follow the commercial open source intellectual property rights imperative.
Superior service is a performance capability that leads to a comparative advantage. Comparative advantages typically can be eroded much more easily than positional advantages and hence this advantage is much more difficult to defend then the positional advantage afforded by ownership of intellectual property.
So, if someone says that using a dual-licensing strategy indicates a lack of ability to provide superior service, it is obviously a tease to give up an important positional advantage. The smart CEO will ignore it.
That said, there are considerations that might make a CEO drop the positional advantage. For example, customers might be less trusting as the profit motive comes across more strongly if you build out your IP position, and customers burnt by IP-based vendor lock-in might hesitate to return to it. Also, it is indeed possible that too strong a positional advantage might make a company more lazy and provide less of a superior service. And so on.
Still, the two types of competitive advantage are sufficiently independent that I would always recommend a company develop and keep them both if they can.