Although the popular discussion of hopefully often refers to "grammar", in fact no general point of grammar is usually at issue — the (now moribund) hopefully controversy was about the usage of a single word. And the genesis of the controversy, as discussed here and here, was clearly a rapid change between about 1960 and 1975 in the relative frequency of hopefully in the evaluative sense "it is to be hoped". However, one of the common rationalizations for this novelty-aversion does raise some grammatical questions of a more general nature.
Bryan Garner (Garner's Modern American Usage, 2009) describes the controversy as follows:
Briefly, the objections are that (1) hopefully properly means "in a hopeful manner" and shouldn't be used in the radically different sense "I hope" or "it is to be hoped"; (2) if the extended sense is accepted, the original sense will be forever lost; and (3) in constructions such as "Hopefully, it won't rain this afternoon," the writer illogically ascribes an emotion (hopefulness) to a nonperson. Hopefully isn't analogous to curiously (= it is a curious fact that), fortunately (=it is a fortunate thing that), and sadly (= it is a sad fact that). How so? Unlike all those other sentence adverbs, hopefully can't be resolved into any longer expression involving a corresponding adjective (hopeful) — but only the verb hope (e.g. it is to be hoped that or I hope that).
Point (1) simply states the complaint. Point (2) is based on the curious notion that English doesn't allow lexical ambiguity, a premise that is spectacularly false in general, and has turned out to be false again in this particular case. Point (3), however, merits further discussion.
Let me note in passing that the examples of curiously and sadly underline the response to point (2). Curiously and sadly can be used as manner adverbials ("watched curiously", "sadly singing") or as evaluative adverbials ("curiously, no", "sadly, yes"), and both of these uses have been common for a long time, without one use driving the other out of the language. The hopefully ex-controversy is about a word-sense difference of a kind that the English language happily tolerates.
And the same examples should warn us not to treat the evaluative senses of these words as solely "sentence adverbs". (I've edited my earlier posts on the topic to avoid misleading phrases like "sentence adverb" or "sentence modifier".) Here are a few examples from the New York Times where sadly and curiously as evaluative adjuncts are used to modify participles, adjectives, predicative prepositional phrases, and even verb phrases:
A great deal of interesting repertory is being sadly overlooked.
She was sadly predeceased by her beloved husband Camillo, …
… even when the book finally appeared in 1966, … it sadly did not receive much attention, …
We learn of the Brady family's happy home life and of the sadly familiar sequence of brutality.
Berger's ailment is sadly in keeping with his medical history.
But when he needed it most, in the touchstone aria "Una furtiva lagrima," it sadly failed him.
This lends the whole production a curiously patriarchal quality.
The campaign signs are curiously familiar, as are the Web sites and even the themes.
That familiar horror-story scenario now seems curiously out of date.
"Capital, Capitals," a brief, chimerical text set by Thomson in chantlike lines with bare-bones accompaniment, curiously felt like an ancestor to Minimalist works like "Einstein on the Beach."
As Albany took a belated first step yesterday toward enacting a bill to give New Yorkers increased police protection in high-crime hours when they need it most, the City Council curiously chose additional delay.
Of course, evaluative hopefully can modify a similar range of things — even in the New York Times:
Newt Gingrich is preparing to make the transition from forgotten-but-not-gone to gone-and-hopefully-forgotten by dropping his presidential campaign next week.
Does one group the protecting pieces around the flag, or use them as a decoy, placing the flag alone in a hopefully overlooked spot?
Runners who carry their phones (hopefully in their pockets, not in their hands) can choose to allow people to track them even when they are off the course.
[Arrive, the Amtrak magazine] always contains a piece in which some hopefully non-controversial semi-celebrity is asked what they love about some Amtrak destination.
“Today was a nice start into a hopefully exciting season, and certainly two promising sessions for us,” said Schumacher.
“We needed a guy to get on base and hopefully score a run to start something up, ” said Johnson.
(Sadly also has another sense as an adverb of degree, meaning "seriously", as in "New York sadly needs to stabilize its property values".)
But even in the case of sentence-level modification, to require equivalence to a phrase of the form "it is a ADJECTIVE fact that S" would eliminate many of the commonest evaluative, epistemic, and attitudinal adjuncts.
"Frankly, this is nonsense" doesn't mean "It is a frank fact that this is nonsense"; "Naturally, I question this argument" doesn't mean "It is a natural fact that I question this argument"; "Surely, he can't have given this much thought" doesn't mean "It is a sure fact that he can't have given this much thought"; "Confidentially, the whole discussion is embarrassing" doesn't mean "It is a confidential fact that the whole discussion is embarrassing"; and analogously for ideally, seriously, thankfully, mercifully, truthfully, ultimately, conversely, and so forth.
With respect to surely, for example, the OED says that it is
Used to express a strong belief in the statement, on the basis of experience or probability, but without absolute proof, or as implying a readiness to maintain it against imaginary or possible denial: = as may be confidently supposed; as must be the case; may not one be sure that…? (The chief current sense.)
This is obviously related to the adjectival sense of sure glossed as "Certain in mind; having no doubt; assured, confident", just as the attitudinal sense of frankly is obviously related to the adjective frank "not practicing concealment", or thankfully is related to thankful. But the implied modification-relations are diverse: perhaps the author is speaking or writing frankly or confidentially; perhaps the author is sure, thankful, or hopeful, or feels that we should all be so.
And in the other direction, a phrase of the form "It is a ADJ fact that S" doesn't always license an evaluative, epistemic, or attitudinal adjunct. Thus we have "It is a bitter fact that S" but generally not (in the relevant sense) "Bitterly, S";
This diversity should remind us of the fact that word-sense patterns — in general and especially across derivationally-related words like sad/sadly and hopeful/hopefully — are quasi-regular.