No. It's not about thinking multidisciplinary. Often times multidisciplinary translates to, "half-assed everything". What I am saying is you have to be able to physically do the basics in everything. And modestly well. There is nothing, nothing that tempers the brain like experiential knowledge. For chemistry, the basic skills include: reading an NMR, looking at a mechanism and say, that makes no sense, running a silica gel column, shooting something down a mass spec... For biology, that's designing an analytical PCR from scratch, cloning (knowing the difference between a K12 and B strain, for example), doing western blots. And you better be able to tell me the chemical, protein structural, and enzyme mechanism differences between arginine and lysine without looking it up - I remember knowing biophysicists who couldn't do that - I remember PhDs who get their training in ostensibly multidisciplinary labs who couldn't do a single thing on that list. Hell, one of them is a Professor at UW Seattle; when he went off to do his postdoc he was scared out of his pants because he went into a yeast lab without knowing how to clone anything because the tech did all of it for him in grad school.
Another real problem is we don't teach students anything anymore on the premise that there's too much to know, and as long as you can look it up, it will be fine. Or if you are working interdisciplinarily, your colleague will be able to tell you (of course they're relying on you too so there's a bootstrapping problem). This is terrible. Sometimes you need to call someone on their bullshit, say during a lecture, or even more importantly during a meeting where actionable decisions are being made and critical insight can avoid wasting time and effort. If you don't have a significant depth of knowledge, which multidisciplinarity typically doesn't encourage - because it's hard - you are just a body making warmth in that room. You need to have instant recall of as much related information as possible at all times when doing science.