In a sense, yes the bound can be violated, but not because is violated, but because the algorithm is completely different. Let me explain.
In Mathematics, elements and rules are defined according to a strict logic and from them, conclusions are drawn following this methodical and univocal logic. It is a milestone of human thinking.
This allows to "mathematize" nature (although historically nature and practical problems have pushed forward mathematical abstract elements). That is, to establish a correspondence between real entities and phenomena based on their relevant similarities to elements in math. In other words, is to say that waves in a pound from a thrown stone are circles, that orbits are ellipses or that quantum states correspond to a wave function.
Once you can establish the connection you can use all the logical conclusions from mathematics to further study and understand nature in a much complex way than simple observation allows, and formulate natural behaviour in form of laws and mathematical relations.
Also you correspond phenomena with problems mathematically formulated, much like establishing that the amount of charge inside a closed surface is proportional to the integral of E through it, or that the shape of a drop is that which minimizes its surface energy.
Finally, an algorithm would be the structured method for solving a mathematical problem, a set of instructions to find a solution to a question formulated in mathematical terms.
That being said, our algorithms reflect our understanding of nature through the best logic we have come up with. But nature already "solves" these and many other problem through mechanisms still out of our grasp.
Nevertheless, we can and have used nature "computational skills" to our advantage, like differentiatig/integrating complex functions instantaneously, or the use of PNN to solve problems that would be very difficult to even formulate mathematically. Humans compute in complex situations really fast things like how to maintain equilibrium, and the our mathematical algorithms for this are still in baby steps.
So answering your question, our algorithms are in a way the best we can come up with to solve a problem that generally has a counterpart in nature. But natural phenomena do not follow mathematical algorithms and are not constrained by this. The question is then, how does nature "compute"? We don't know yet.