I play nothing but bot games and featured game modes, and I regularly see teams with two or more skinned champions (including me on occasion), and have had up to four skins on my team, and I rarely have a team with no skins (which happens mostly when the majority of the team is playing a free rotation champion). I noticed this because, no matter how many skins the player team has (without hitting the five max), the bots tend to have exactly one more.
Edit: For example, two back to back games I just played tonight had (1) Subterranean Nautilus, Warring Kingdoms Zin Xhao, Zilean (me), Malphite, and Hired Gun Lucian (2) Frozen Terror Nocturne (me), Nami, Heartseeker Ashe, Akali, and Grave Lord Azir.