According to Vester (1991; see the full reference below), the gerund can take an object in the following contexts:
genitive: ars scribendi (epistulam)
ablative: scribendo (epistulam) tempus tero
nominative: mihi (epistulam) scribendum est
According to Vester, "it is evident that scribendum is a gerund in mihi epistulam scribendum est, but for some scholars it is less evident in mihi scribendum est" (p. 297). So note that the strong statement in your post above ("one cannot say aquam bibendum est") is not correct (according to some scholars), although it is true that such a statement is found in some/many Latin grammars. In fact, there are some few attested examples of this usage: agitandum est vigilias (Pl. Trin. 869); aeternas poenas in morte timendum est (Lucr. 1, 111), i.a. See also some further discussion & comments in this post.
More interestingly, Vester also points out that the gerund cannot take objects in the following contexts:
dative: aptus scribendo (*epistulam)
in+ablative: in scribendo (*epistulam) obdormivit
ad+accusative: paratus ad scribendum (*epistulam)
As for your questions ("How strong is the rule? That is, do we have strong evidence that the Romans always obeyed this rule? Do ancient authors always follow this rule?"), the prohibition of using objects with gerunds is, for example, very strong in in+ablative and ad+accusative contexts across authors of different periods (and for me this is a very interesting issue: there must be a grammatical explanation accounting for the absence of objects in these particular contexts, an explanation that, by the way, is not provided by a functionalist linguist like Vester). As for other cases (the first ones above), the norm varies across authors: e.g., the gerund in ablative often takes objects in Vitruvius, less so in Sallust, and much less so in Cicero (cf. the data and percentages in Vester (1991)).
As is well-known, it is often stated in many Latin grammars that one can say/write cupidus videndi urbem (gerund) and cupidus videndae urbis (gerundive). However, when one looks at the data & percentages, one realizes that there are some important differences across authors of different periods: the usage of gerund+object in this context is more typical of Early Latin than of Classical Latin, where the gerundive is by far much more used.
To conclude, if one is not interested in these philological differences of usage (e.g., the usage of non-prepositional ablative plus object is typical of Vitruvius but not of Cicero, the usage of aquam bibendum est is not typical but it is found in ...), the simplified rule for learners/"speakers" of Latin is to use the gerundive instead of the "gerund plus object" (except under the well-known circumstances pointed out by TKR and Joel Derfner. For a nice summary of these circumstances, i.a., I recommend the reading of the excellent chapter XVII "The Gerund and Gerundive" (pp. 157-166) by E. C. Woodcock (1959). A New Latin Syntax. London: Methuen).
VESTER, ELSELINE (1991). "Reflections on the gerund and gerundive". In Robert Coleman (ed.). New Studies in Latin Linguistics. 295-310. Amsterdam/Philadelphia: John Benjamins.