Why the material changes the result
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Leaching: the container adds something
Material migrates out of the wall into the sample. Glass can contribute sodium, boron and silica; plastics can contribute plasticizers and trace metals from processing. If you are measuring something at trace level and the bottle supplies it, the result is high and looks real.
Adsorption: the container removes something
Analytes stick to the wall and leave solution. Metals at low concentration are the classic case, which is why acid preservation is specified for them: it keeps them in solution rather than on the glass. Organics adsorb onto plastics the same way.
Permeation: the container lets something through
Gases and volatile organics pass through plastic walls in both directions over time. A volatile sample in a permeable bottle loses analyte to the air; a clean sample stored near solvents can gain it. Glass and fluoropolymer are the answer where this matters.
Which is why the regulation names the material
Table II does not say "a suitable container". It gives codes, and footnote 1 defines them: P for polyethylene, FP for fluoropolymer, G for glass, PA for a sterilizable plastic, LDPE for low density polyethylene. The regulation is specifying the polymer.
Clean is a specification too
For trace work the container has to arrive at a known cleanliness, and certified pre-cleaned containers exist for exactly that. Washing a bottle yourself and assuming it is clean enough for trace metals is a common and invisible error.
None of this announces itself
A leached, adsorbed or permeated sample looks completely normal. There is no cloudiness, no smell, no sign. That is the reason the container is specified in advance rather than judged afterwards.