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If there's only one grocery store, maybe. But that's a monopoly, and that's going to be shit no matter what. Ideally you have multiple grocery stores that compete, and if one raises prices the other will take their customers. (If they all coordinate to raise their prices, that's a cartel and that's also bad.)

So you're not really exposing a problem with UBI, but rather with unregulated capitalism.

I'll humor this, even though I'm tired of answering this same question. I'll do you a favor and give you the short version, first: Inflation has nothing to do with how currency is distributed and everything to do with the supply of currency in circulation. Now that we've established the basic concept, let's break some of it down. If there's $100 in circulation, it doesn't matter if one person has all of it, or 100 people have $1. The value of $1 is the same. If $1000 is in circulation, then $100 is worth less than if only $100 is in circulation, even if one person has $901 and everyone else has $1. Why is this so difficult to understand? Why do you believe that money is somehow worth more if its distribution is unequal? If people buy more stuff, that's called a healthy economy. If people buy 'too much milk and the prices go up' then someone will sell milk for less to undercut the competition in a healthy economic system. If you can't sell it for less, you innovate. If you can't innovate, or sell for less, then you can't compete and you lose. Everyone being able to afford more milk doesn't cause $1 to be worth less. Of course, this example isn't realistic anymore, but that's due to capitalism failing -- the underlying principals of the example still hold true.