The generally accepted rule of thumb is not to have two resident applications of the same type/classification, since MBAM isn't an anti-virus it shouldn't be an issue with a resident AV. The same would apply to having two resident anti-spyware applications.
I haven't got the slightest idea why they would say that, personally I would be asking why and looking for detailed answers.
There are many avast users that also use MBAM Pro without issue.
You only need to look at my signature to see I also run SAS Pro (resident anti-spyware) and no issues with avast. I also have MBAM free so on-demand, but then again no problem.