Learn English – the phonological error pronouncing /θ/ as /s/ called

No, there cannot be. Phonemic /e/ at the end of a word in English can only occur as a phonetic falling diphthong [ej], as in say or they. That’s why those have a ‹y› in our spelling today, and why sleigh has an ‹i› in it.

And unstressed /ɛ/ will soon enough go the way of all things, despite what bokeh enthusiasts would have you believe. (Same with the meh-sayers.) Because English phonotactics forbid an open /ɛ/ at the end of the word, those will therefore soon enough become either a phonemic schwa /ə/ — or else become a close vowel like /e/ or /i/ phonemically and so one with the characteristic falling phonetic diphthong [ej] or [ij] required by English phonotactics.

I therefore little doubt that the word currently spelled bokeh will end up /ˈbokə/ just like the boca heard in the city of Boca Raton, Florida, to rhyme with mocha.

The other two possibilities are for bokeh to wind up rhyming either with hokey or else with hockey. This would be like how Spanish chile which ends with /e/ becomes in English chili which ends in /i/.

Only if the second syllable became stressed could bokeh become /boˈke/ or more likely /bəˈke/, which is the sort of thing you get when in English you pronounce the Spanish word olé under English phonotactic rules.

Whatever happens to words like bokeh as they assimilate to English, they will need to be respelled to use a spelling similar to whatever words they end up rhyming with in order for them to be predictably pronounced by monoglot English readers.

Probably spelling what is now commonly rendered bokeh in English as boka would have been better from the get-go.

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.