Should the O in Russian be pronounced as a short A (like a short A as in English)?
To be more precise, after non-palatalized consonant pronunciation of unstressed "o" is reduced, this is called
аканье (akanye) in Russian, it's quite an old phenomena which can be tracked back for at least 500 years. There's an article from wikipedia about this, and this particular quote is relevant:
In Russian (except for Northern dialects), /o/ and /a/ phonetically merge in unstressed positions. If not preceded by a palatalized (soft) consonant, these phonemes give [ɐ] (sometimes also transcribed as [ʌ]) in the syllable immediately before the stress and in absolute word-initial position. In other unstressed locations, non-softened /o/ and /a/ are further reduced towards a short, poorly enunciated [ə]. After soft consonants, unstressed /o/ and /a/ are pronounced like [ɪ] in most varieties of Russian (see vowel reduction in Russian for details); this reduction is not considered a manifestation of akanye. Unlike Belarusian akanne, Russian akanye does not affect softened vowels.
As a side node, actually in English we can encounter sort of same thing in a lot of dialects where, say, "stop" is pronounced as [stʌp].