As other folks said, getting a K-1 has nothing to do with whether you received distributions.
However the post saying that if you hold for only 1 day you will get a (non-zero) K-1 is also not always true.
The MLPs mostly seem to do their accounting at month end, so if you have a short holding period which does not cross a month end you may not receive a K-1 (or receive one with all zeros).
However if you hold over a month end you are guaranteed to receive a K-1.
"My guess is NO"
Your guess is WRONG. If you own KMP for even a single day, you will get a K-1. Your share of the partnership's income/expenses is a function of your ownership for a specific period of time, not whether or not you receive a distribution. The distribution is just one item that is listed on the K-1 that affects your capital base.
Cash distributions have nothing to do with whether or not a K-1 gets issued to you. The income is split between the partners based on how much they own & for how long, not on who got how much cash. Completely different than owning a corporation & getting dividends.