It's an excellent point, and one that begs the question of just what, precisely, culture is, at least archaeologically speaking.
Archaeologically, we use the term "culture" to describe related artifacts and groups of artifacts the consistently appear in a given place and date to within a given range of dates (so, the Clovis Culture appears in North America and dates to about 13,000 years ago and consists of sets of artifacts that include the distinctive Clovis Points. Based on the similarities of tools and other artifacts, it is generally assumed that the different sites at which these artifacts are found are related to the same or similar lifeways (the same tools=similar tasks, the thinking goes), and as such it makes sense to groups these sites and their assemblages together.
The archaeologist V. Gordon Childe, who is often considered one of the popularizers of the use of the term "culture" in this way, wrote:
We find certain types of remains - pots, implements, ornaments, burial rites and house forms - constantly recurring together. Such a complex of associated traits we shall call a "cultural group" or just a "culture". We assume that such a complex is the material expression of what today we would call "a people".
One problem is that these perceived cultures may be partially a product of the archaeological record rather than simply direct evidence of actual cultural groupings or peoples. For example, the Clovis Point seems to represent the remains of a highly mobile nomadic culture that engaged in, and likely was reliant on, big game hunting. And likely this was the case for most of the early American peoples. But there are numerous artifacts used by people that simply don't preserve, or at least rarely preserve, in the archaeological record, and so we are not seeing many of the tools, art, social signifiers, and other objects that would have been vital to the day-to-day lives of the Clovis peoples, and that's not even getting into the intangibles such as language, religious beliefs, social organization, etc. Some of this information can be teased out of the remains to varying degrees, but not all of it, and never with 100% confidence. We're putting together a jigsaw puzzle with several of the pieces missing. For this reason, many archaeologists refuse to use the term "culture" to describe the artifact groupings, opting instead for more accurately descriptive terms such as "technology-complexes."
Of course, the degree to which archaeology can describe an actual culture varies greatly. With the Clovis complex, we know little other than that they all used similar spear points and appeared to make extensive use of large animals for food and tool material. We can actually derive quite a bit of information from that, and speculate on quite a bit more, but there is so much that we can't know that it is fair to say that we may just as well be looking at many different cultures spread throughout North America who all used similar projectile points as to say that they were all related to a "stock" culture and shared a good deal more than hunting practices and nomadic land use patterns. Some may have been more reliant on hunting than others, there were probably multiple dialects, maybe even many different languages, and if it turns out that Clovis tool-making methods spread to many different groups of people already in North America (much as we know that later tool-manufacturing methods spread in the Americas), then it is entirely possible that there were multiple languages, religions, and regionally highly-adapted lifeways. In other words, Clovis may represent a solution to a common problem rather than a common culture.
By contrast, the Maya had such distinctive tools, architecture, and writing that we can say with confidence that there was a shared culture, likely a shared ethnicity, amongst the people living in Mayan sites. Even there, there is likely variations (some of them possibly quite important) that we are simply unaware of, but it is more reasonable to talk about "Mayan Culture" than "Clovis Culture." And these are two extreme ends of a spectrum.
Another problem is that artifacts that are perceived as being separate are sometimes actually closely related, and those perceived as being closely related might, on further analysis, prove to be separate. For example, in reading archaeology journals published in the 1920s through the 1950s, it's common to see certain types of artifacts grouped together as being part of the same "culture", distinct from other groupings of artifacts. After the 1950s, as radiocarbon dating became common, it was not unheard of for some of these "cultures" to turn out to be from the same time, not just the same place, and likely represent the remains not of separate cultures, but of separate work places or task sites belonging to the same group of people. While this wasn't too common, it did occur, and is a lesson to be kept in mind.
In the end, talking about archaeological "cultures" can often be nothing more than what my professors referred to as "confusing people with pots" - assuming that the recovered artifacts are more strongly indicative of the people who used them than they really are. If you are reading about archaeology, or watching a documentary, be aware of how the term "culture" is used - is it used to describe a group of people who are known to have shared a common identity - such as the Maya - or is it used to describe a set of artifacts without regard to how closely the people using them were related. It gets used frequently in both ways, but the two uses are not interchangeable.