Phrases and Meanings-III : Drop in Any Time

I wish this phrase "Drop in any time" would only make up its mind about what it means. Most of us know that the dictionary is meant to be ignored and sort of pick up meanings by usage - but, heck, that can be done only for phrases that maintain some sort of constancy in usage. When a phrase is so indecisive about exactly what it means it really gets on my nerves.
An early experience had taught me that this phrase was a meaningless politeness similar to 'Nice meeting you' (which, when someone uses it with me meant, "The nicest thing about meeting you is parting from you and the solacing thought that I shall never meet you again"). It meant nothing more than the fact that the concerned people were not actively repelled by you - yet!
Those were the days that I used to take the printed word as gospel (being days in which newspapers could still be relied upon to give the facts) and the dictionary was my sole guide for meanings. So, when a couple I met said "Drop in any time" just as we parted, I thought I had found a new caring family in an unknown city. There I was hair in a braid - as Wodehouse would put it - sunnily smiling at them as I walked into their home on a Sunday. Within five seconds, I had learnt what 'being given the bum's rush' was all about. It meant that your hostess tells you in gushing words how sorry they were that they were having family coming in any time while your host has his arm around your shoulder and is nudging you towards the door inexorably. Before your bewildered mind can comprehend exactly what you are hearing you are not merely outside the door but outside the gate which your host is busy padlocking while your hostess utters a last apology and a sweet goodbye.
The subsequent days taught me the meaning of more phrases. For example, I knew that 'one taking the high road and the other the low road' meant that if you happen to meet the host of that day coming towards you on the pavement, you would see him instantly find some pressing business on the other side. Why, he will even risk crossing the road despite high speed traffic in order to attend to it. Someone cutting you dead means that if you run into your hostess in a party then, while you are bleating "Hello" in her ear she would dreamily hear a whisper of a thought from someone across the room and rush to answer it. Enough on that subject. In addition to teaching me the meaning of all sorts of phrases, it also taught me that "Drop in any time" does not mean what the dictionary says it means.
Ah, by the way, these were in the days when a telephone connection depended on your knowing someone related at least to the Telecom Minister's peon and when mobile telephony belonged in the realms of Science Fiction. People still used to just walk into someone's house saying, "I was just passing this way and thought I would meet you" even if their host's house was the lone one in the middle of nowhere and they had to trek 8 Kms to reach it. (Before you ask me, YES, I am THAT old.)
If only one could hold on to that meaning for "Drop in any time", all would be well. I mean you would just say "Sure" to that phrase and forget all about it. Unfortunately, the damn phrase switches meanings every now and then. I have had hostesses accost me in a wounded tone, "I invited you but you never do come". (I know, I know! It seems incredible that anyone could at all be THAT hungry for company that they would miss me but will you please wait before you call me a liar?) I have never managed to understand whether this meant that their "Drop in any time" was a genuine invitation or was it only a means of taking the moral high ground of having invited me without running the risk of actually having to host me.
With such an indecisive phrase, it is only right that I choose to assign the meaning to it myself. So, I have decided that I shall accept as an invitation only when someone says "Drop in at this time". "Drop in any time" shall, for me, mean that if I acted on the dictionary meaning those people would only mean, "Drop Dead" in future regardless of what they say.
How about you?