(I am aware DNA is said to point to a common origin for all life on earth, but is that really certain either? Or just a good construction on the basis of the current understanding?)
I assist with bioinformatics at a lab studying evolutionary biology. The probability that Humans and Chimpanzees share a more recent common ancestor than Gibbons, Gorillas, and Baboons is so high (or for many other phylogenetic analyses), that we might as well call it “really certain.”
Studying the DNA relationships between organisms and determining how they are related by common ancestry commonly uses Bayesian probabilities. In this statistical framework evidence (data) about whether something is true or not is expressed in terms of degrees of belief, how certain something is to be the case.
So with common ancestry as mentioned above, there is a very high probability that humans and chimps share a common ancestor.
So no, in this specific example, I cannot say with 100% certainty that humans and chimps have a common ancestor. However, when you take this evidence and combine it with other forms of DNA evidence, and especially other independent fields of science all coming to the same conclusion (common ancestry), it becomes very difficult to see evolution as anything other than a scientific fact, an observation that has been repeatedly confirmed and accepted as true. Such trueness is provisional of course, since it can be improved upon.
Think of it this way. Gravity is a scientific fact. Has been that way back in Newton’s day, through Einstein’s, and up to our day. Yet, the specifics about gravity have changed overtime. What people accept as fact in the 1800s has changed. But the underlying fundamentals have not. Common ancestry is just one of those fundamentals. It’s a scientific fact.
