Sir Charles Fawcett, a British historian writing in 1937, published an article (which can be found here, although there's probably a more authoritative source) considering this possibility. His conclusion was that it was likely that the flag was deliberately chosen, but while there is evidence that there were more records about it, those records no longer exist and so it can't be confirmed.
Some excerpts (emphasis mine, and some spacing added for readability):
The thirteen stripes of the National Flag are thus undeniably derived
from the Grand Union Flag. Their origin in the latter is more
controversial, but the position is at any rate clearer if that flag
was exactly the same as the East India Company's ordinary flag between
1707 and 1801. The adoption of an English flag with the Union Jack in
its canton gives rise to no difficulty. Though hostilities began in
1775, it is indisputable that Washington and other leaders of the
revolt were still in hopes of a reconciliation with the
Mother-country, and the war was regarded as one against the unlawful
acts of the King's Ministry rather than one involving disloyalty to
the King. Otherwise it is absurd to suppose that a flag with the Union
Jack on it would ever have been adopted.(36)
...
[The East India Company's] striped flag had been flying for
nearly two centuries, and it would at any rate be familiar to
Englishmen. It seems probable that it was also well known to American
seamen, who made voyages to Dutch and other European ports for various
purposes, including the large traffic in smuggling tea and other
heavily taxed goods into America(63). Thus Esek Hopkins (1718-1802),
who was commissioned in December 1775 as Commander-in-Chief of the new
navy of the thirteen States and on whose flagship the Grand Union Flag
was first hoisted would almost certainly be acquainted with it, for
not only had he been one of the leading colonial seamen, but also a
privateer captain, who had made brilliant and successful ventures
during the Seven Years' War (1756-63).
The distinguished American
leader, Benjamin Franklin (1706-90), was another who must have known
of it. He came to London as a young man to finish his education as a
printer (December 1724 to July 1726), and made two other long stays in
England from 1757 to 1762 and from 1764 to 1774. During the latter
period he acted as London agent for the opposition to the King's
Government in four of the American colonies. In 1761 he made a trip to
Holland and during his third period of residence he visited France and
Germany. He thus had opportunities of seeing the Company's flag;(64)
and even if he did not himself see it, it did not need the omniscience
of Macaulay's schoolboy for him and hundreds of other English settlers
in America to know of it.
He would naturally be interested in the East
India Company, for (in addition to its prominence as a mercantile
body) it was concerned in the agitation that was going on in the
American colonies. Thus in a letter of 5 January 1773 Franklin
[writes a letter against taxing tea, which is the Company's position as well].
Franklin, therefore, far from having reason to dislike the Company,
could properly regard it almost as an ally. Another thing that might
dispose him to favour its flag was that it symbolized independence, in
the sense that the Company's administration in India was not then
directly controlled by the King's ministers, for it was not till 1784
that the well-known "Board of Control" was established. Franklin was
Chairman of the "Committee of Conference", consisting of himself and
two others, which was appointed by the second continental congress on
15 June 1775 to confer with General Washington on the organization of
the land forces.(68) He is likely, therefore, to have had an
influential voice in settling their flag. He is also said to have
designed the Rattlesnake flag of South Carolina.(69)
All that said, Sir Fawcett continues:
In the absence of due substantiation for the alleged speech of
Franklin in its favour, this is as high as I can reasonably put the
case for the view that the Company's flag was deliberately copied by
the designers of the Grand Union Flag in 1775.
In the end, he concludes:
The present tendency in the United States is to treat the origin of
the Grand Union Flag as a mystery, which is unlikely to be solved(76).
...
In any case I think my research about it has
clarified some points that were previously obscure, or have been the
subject of erroneous statements; and I trust the publication of this
article may result in further light being thrown on the subject by
others more competent than I am to discuss points about flags.
It's worth considering the source here - a British historian could easily have a bias towards finding that the nascent US borrowed much from the British - but the article seems well written and referenced to my inexpert eye. Thus:
TL;DR
There is no remaining documented evidence as to why, but it's very feasible that Ben Franklin could have pushed for or chosen the East India Company's flag as the Grand Union Flag to be a convenient symbol of independence from the British crown. The stripes on the first official US flag would then have been a carry-over from the Grand Union Flag, but not explicitly tied to the East India Company.