True, but the second implementation may use different, well-tested, mature code.
If the first lab used C++, and the second lab used Matlab and its libraries, and the third lab used trusted code based on NumPy, I would be surprised if their errors were strongly correlated. Brand new code? Sure. But not code they've used for several years through multiple experiments, or code that's part of a widely-used software package.
The thing is, labs working in similar areas most likely have ready, tested, trusted software toolkits for doing similar tasks, especially when it comes to data analysis.
It may seem to a programmer that the fastest, easiest thing to do would be to read the code, in fact the fastest, easiest thing to do is probably for another lab in the same field to do an independent analysis of the data with their own code.