Yes it is true. According my my grammar dictionary, [Verb in 連用形 + に] can only be used with motion verbs such as
出る to mean "to go/come/motion-verb (in order to) do something". The "In order to" becomes explicit when の為に is used, indicating a rather important purpose.
Let me try to break down the composition:
*any verb or い-adjective can become a noun when placed in 連用形. This is similar to the English concept of "gerund". E.g.
talk is a verb.
talking is also a verb. But in the sentence "Is my
talking distracting you?"
talking here is a noun.
に as a particle indicates a point of space/time/reasoning.
から which is a half-line with a start point; from a point in space/time/reasoning)
まで, which is the other half-line with an end point; terminating at a point in space/time/reasoning)
And let's also take a motion verb:
Then let's try to piece it back together:
** because 行く goes towards whatever is marked by に
Now let's try for your example:
遊びに食べる (To eat, at the point of reasoning of "a playing"). It cannot be naturally parsed because に does not relate the thing it marks with the verb 食べる. Unlike に+motion verb, whatever に marks is directly related to the motion verb.
The act of eating has nothing inherent to do with the playing. On the other hand, moving has an inherent connection to the destination. See sawa's explanation of に in "に and で revisited"