In isolation, yes. But no one would write E7 F#øA. Writing E7 Ami6 explains the clear dominant-tonic relationship. In this case, context makes it completely unambiguous. Just saying. 
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This is false. This claim only holds up if one simply thinks “vertically* (and under the assumption that only tertian syntax is valid), but not if one actually listens musically.
If the Count Basie Orchestra plays an Ab6 chord in bars 1–3 of a blues in Ab, to claim that it’s actually an inverted Fmin7 chord in first inversion is meaningless on any level beyond the most limited and pedantically syntactical.
There is no ambiguity as to tonic function of a maj 6 chord when approached through a PD - D progression like II - V - I6.
If you want actual musical ambiguity, listen to something like the opening of Beethoven’s first symphony.
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… and as we are talking about chord symbols, Ab6 makes it perfectly and unambigously clear, that Ab is considered to be the root by the composer (or, at least: the engraver).
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But what about Basie’s big hit Jumpin’ at the Woodside in the key of Gm7/Bb? 
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Just think in vertical intervals and everything is a piece of cake 
Happy holidays!