I think a more apt analogy would be saying you are a grand master in chess but can't explain the rules for how to move a rook.
As Feynman said: It is like a chess game. If you are in a corner with only a few pieces involved, you can work out exactly what is going to happen, and you can always do that when there are only a few pieces. And yet in the real game there are so many pieces that you can’t figure out what is going to happen ... There is such a lot in the world. There is so much distance between the fundamental rules and the final phenomena that it is almost unbelievable that the final variety of phenomena can come from such a steady operation of such simple rules.
The scientists that mrjangles derides, who "claim to understand the structure of the universe", sound to me like physicists claiming they know the base rules of the game. (I'll set aside that nobody has cracked, say, quantum gravity yet).
When we talk about the puzzling mysteries of the structure of glasses, or superconductivity, or turbulence, or so on -- most of those aren't a matter of a lack of understanding of the base rules of the universe, but rather their consequences when applied to a big system with a lot of parts. That's knowing the rules for how rooks work, but being surprised when your opponent captures your queen with one.
What this means is that we discovered that the structure and order, as we see in particle physics, actually appears everywhere in nature. For example, vibrations moving through a solid (such as when you tap the table in front of you) actually behave exactly like (what are incorrectly named for historical reasons) "fundamental" particles moving through space. They interact with each other mathematically with the exact same equations. Recently scientists even created a material which these "quasiparticles" (as the excitation are called) obey the laws of special relativity inside the solid, except the speed of light is replaced by the speed of sound in the solid.
All this probably reached its peak when the Higgs mechanism, and indeed pretty much the the entire theory between the Higgs particle, was discovered by P.W. Anderson in superconductors. He suggested that perhaps the same mechanism is what gave particles in the standard model their mass. He was proven correct, but the Nobel prize went to Higgs for historical and political reasons, and also because P.W.A already had one Nobel prize.
Now days high energy particle physics views space as a kind of medium, and the electrons and quarks etc as just being the particular manifestation of whatever chaotic thing is going on underneath (more particles or who knows what), which is meant by "effective theory".
Anyway, the point is that no, it isn't that case of a few fundamental rules are controlling everything. We now have a much better picture and it seems to be order and chaos appearing in all different scales in all different manner of ways and to understand each manifestation one needs to start a new each time.
Phillip Anderson's famous article "More is Different" from 1972 was the first to really espouse this point of view. It has become sort of an anthem for many scientists. https://www.tkm.kit.edu/downloads/TKM1_2011_more_is_differen...
In other words, once there are enough pieces on the board, you get blindsided as your queen is captured by a rook in a move you never saw coming, even though in retrospect you can go back and see that, yes, the rook really did move in a straight line.
That's why, even if biology really is "just" applied chemistry and so on, you'd never predict the wonderful behaviour of biology if you had only studied systems of less than ten molecules.
And I don't think Feynman would disagree at all, nor would he claim that knowing just the basic laws of physics would let you anticipate the character of cell biology or turbulent fluids, or all the other wonderful systems that have nontrivial degrees of freedom.
Perhaps a better analogy would be: Someone who claims to be a chess player, but keeps getting disqualified from tournaments for making illegal moves.
For example, when it comes to QCD and the structure of the nucleus, we have no idea if our theories are correct or even make sense. One of the millon dollar Millenium prizes is currently being offered for anyone that can prove the equations of QCD are even well defined or if it is possible to even have a bound state (i.e for particles to exist at all) within a QCD framework.
So my point is the underlying theory is really only described in the perturbation theory setting. I.e., in the high energy limit (smashing things together). Now the equations and mathematics behind QCD are very attractive and probably contain a great many aspects of what we will eventually become the full theory, but until we can predict, for example, the mass of a nucleus from those equations (or anything at all whatsoever), then they are certainly not proven.
So far all we know is that these equations can predict what comes out (and in what direction) when we smash particles together.
But, given you've given a whole spiel about about EFTs, you can think of the lattice formulation of QCD as an EFT whose cutoff is the lattice spacing. We can compute the mass of hadrons and take the continuum limit / cutoff to infinity. And when we take that limit holding some physical hadronic observables fixed, the spectrum matches perfectly. So I think it's relatively unfair and misleading to say that because we can't do it with pen and paper we can't make any low-energy QCD predictions at all whatsoever.
What always drives me crazy about stories like the OP is that strongly coupled theories are automatically technically natural. But most phenomenologists don't like them because they, not being proficient supercomputer programmers, can't calculate anything.
However, that was over 7 years ago, and someone else in the comments linked an article talking about the breakthroughs since then, and they seem significant, so things may well have improved since then.
Regardless, lattice QCD has always been real science and always been quite impressive. Any direct attempt to match theory with known experiments always is real science regardless of whether you agree with the methods.
Indeed, this is more like a fifteen-year-old understanding. For example in 2008 , the authors of https://inspirehep.net/literature/804184 tuned to reproduce the pion and kaon masses (to fix the quark masses) and then predict ~ a dozen further masses, and in 2015 they computed the proton/neutron mass splitting https://inspirehep.net/literature/1300659 . In https://inspirehep.net/literature/1675748 we reproduced the nucleon axial coupling to ~1%.