People who say such things are glass-half-empty people, I say!
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I'd really say that flanking, OAs and push/pull/slide are the biggest "offenders" of the battlegrid need...with those things taken care of, I see no reason why you'd need a battlemap (I still recommend mapping the locations fairly accurately in size for your own notes though).
That said, I love battlegrids more and more in 4E, but obviously YMMV.
Seems like there are two basic ways to approach this one.
One way is theoritically, as in the really cool post partially quoted above. The other is emperically, by playtesting for a good solution. Of course, both work together, but can separately provide two distinct starting points.
1. Theory
For the theoretical method, you could try to find a way around the (3) issues of flanking, OA's, and push/pull/slide. One way to finesse that challenge is to look past the simulationist or gamist element of the (3) issues, and to their effects only.
Flanking offers combat advantage. OA's threaten certain moves with a reprisal. Push/pull/slide allow you to improve your positioning vis-a-vis your opponent.
In a way these are all the same effect. You and your allies all want to be in a position to threaten all of your enemies, with +2 for combat advantage, while at the same time avoiding allowing the enemy such benefits.
So, for example, whenever you would use a power that allows you to pull an opponent, then you can tell the DM you will use that to place them in a flanked position with your striker, for instance. Then when that enemy tries to move away, you may claim an OA.
2. Playtest
Now either as a follow-along to the above, or as a starting point before the above (doesn't much matter which) you can also take the empirical route.
If you have already done the theory work (above) then the rest is a matter of convention or house ruling. If your gaming group has vivid imaginations, it could be simple enough. Then DM need only adjuducate disagreements.
If there is too much disagreement, then you could need some sort of diagram as to who is flanking who and so on. You could list it on your initiative chart. Same plce you would put modifiers such as marked, and hunters quarry.
If you prefer to skip the theory and go straight to the playtesting, then please start --- on the battlemat! Yes, have your group try the battlemat if they have not already, please. It is very cool. But if like most gropups you have been there done that, then go ahead for the moment and stay there.
While some (the rest?) of the group is using the battlemat, you (and others?) just stick with the imagination. You will find that this playtest allows development of most oif the conventions you will need.
As you "imagine" the battlemat one way, and the actual battlemat is in fact slightly different, then you will work thru the wrinkles as you go along. Soon (group and DM willing) you will be mapless.
Perhaps the glass is already half full after all !
