So, yes, your friend is mostly right. However, this is a very general feng shui statement as there are different variations of a staircase facing the front door, thus creating different feng shui scenarios.
The feng shui case of a big foyer with many grounding architectural features and the staircase far from the front door will be very different from a feng shui case of a small foyer with stairs closely facing the main door.
In case of a big foyer with a staircase further from the door, the energy can settle in and nourish the space, gradually and harmoniously finding its way to other areas of the house. When the foyer is small, though, and the staircase is facing the main door directly, the energy takes a rushed and fragmented quality, being forced to quickly rush up or down the stairs.
The feng shui cures in these cases are focused on creating a feng shui decorating style at the main door that will slow down the energy, focus it and then guide it to all areas of the main floor. This can be achieved with strategically placed art, specific colors, a big plant or a vase of flowers, specific pieces of furniture or mirrors (please note that mirrors should never face the entrance directly, as this pushes the energy away instead of drawing it in.)
=> Feng Shui Cures To Ground the Energy of a Staircase
=> How To Create Good Feng Shui in Your Main Entry
=> Feng Shui Decorating Tips
The feng shui cures will be specific for each space, and if your floor plan has staircases too close to the main door, it is always wise to seek the advice of a professional feng shui consultant who will chart the flow of energy and give you helpful recommendations to improve the flow of Chi.
To summarize, the staircase facing the main door presents a similar feng shui challenge to a back door aligned with the main door. In both cases, the Chi is forced to leave the space quickly and is not given the opportunity to settle in and harmoniously nourish your home.