Since the actual question here is very easy to answer (the answer is no, there is no truth whatsoever in her statement), I will instead comment a bit on why it really is that methane has two varying pronunciations.
Note that this is not merely a BrE vs. AmE thing—while AmE generally only has the pronunciation with the short e, BrE has both.
Methane is derived from methyl + -ane (used in chemical compounds). Methyl itself is back-formed (originally in Swedish) from methylene. This is ultimately based on the Ancient Greek word μεθύ [meˈθy] ‘sweet wine’ (cognate with English mead and Sanskrit madhú-, all from a root that just means ‘sweet’). Note that Greek ε is a short e.
The back-formation of methyl from methylene was based on the very similar-sounding pair of ethyl and ethylene, which was just a few years old itself when methyl was back-formed. Ethyl was formed in German, from the base of (a)ether + -yl (used in names of chemical groups).
Ether itself is from the Ancient Greek αἰθήρ [aiˈθɛːɾ] ‘upper layer of the stratosphere’, which has a diphthong /ai/. This diphthong regularly (through Latin ae and Old French é) yields a long e in English.
In other words, etymology means that we should have:
Meth- [mɛθ-] with a short e
Eth- [iːθ-] with a long e
But there are so many pairs between the two—(m)ethyl, (m)ethylene, (m)ethane, etc.—so it’s not that strange, really, that people started getting their long and short e’s mixed up a bit, particularly when you remember that the long e in eth- is automatically shortened in words where it loses its stress, like ethereal.
In AmE, this confusion has mostly meant that the long e of eth- has been shortened except in ether itself: ethane, ethanol, ethyl, and ethylene all tend to have a short e, unetymologically. The short e in meth- has been retained.
In BrE, the confusion is more random: eth- tends to have both long and short variants in many derivations, but not all (ethanol, for instance, always has a short e, and ether itself always has its etymological long e); while meth- has taken over the long e in some derivations, but not all (e.g., methane always has a long e, while methanol always has a short e).
Pure transatlantic chaos, in other words.