Learn English – “Who” versus “whom” with multiple verbs

For sentences structured like the example - you are right, context (and pragmatics) are all: without any context to suggest otherwise, "buy" needs an object, so the object must be shared, and since "football and cricket" is not a suitable object for "drink", we understand the intransitive sense of that verb (to drink alcohol).

For situations where confusion might arise, there are plenty of possible strategies to make it clear what is intended, for example:

I like to buy fish and chips and eat it.

I like to drink and I like to watch football and cricket.

I like to drink while watching football and cricket.

I like to watch football and cricket and drink. (here we assume the speaker doesn't like watching drink!)

I believe both of these sentences are correct, but that they convey slightly different shades of meaning.

Terrible Mr. Brown set my boat on fire.

Mr. Brown set my boat on fire; I think he's terrible.

The terrible Mr. Brown set my boat on fire.

Mr. Brown, who is infamous in these parts for being terrible, set my boat on fire.

When the adjective is "US-based" rather than "terrible", there is really very little difference in meaning between the two sentences. Putting "the" in might make the company sound a little more well-known.