Just to clear-up some things: General Sykes also does not have an equestrian monument on the field at Gettysburg. He commanded the Fifth Corps of the Army of the Potomac. Sickles has a small monument where he was wounded near the Trostle Barn. A short walk from United States Avenue where one can park a car and then proceed up a drive on the west side of the barn. The monument can be located there.
Now, just to "muddy-up" some things: When Berdan's sharpshooters (1st Regiment USSS) and the 3rd Maine advanced into Pitzer's Woods, they did not encounter Longstreet's men. Rather, at that point they actually engaged Anderson's Division of A.P. Hill's Corps moving into position in a brief firefight before withdrawing. I suspect that the information they disclosed passed through the chain of command and got to Sickles whose experience just a few months previously at Chancellorsville induced him to advance his line forward beyond the position contemplated by General Meade. Keep in mind that Sickles held an excellent position at Chancellorsville (Hazel's Grove), but when General Hooker ordered him to vacate that high ground, the Confederates posted artillery there and were able to link their otherwise disjointed battle lines together to finish off the Federals. There is no question that Sickles disobeyed Meade's orders, regardless of his motivation. The remaining question is whether, inadvertently, his forward movement actually saved the Federal position on Cemetery Ridge. Several points: Neither Meade nor Lee realized where the flanks of their opponent rested. Unlike us today, neither Meade nor his subordinates knew Lee's plans at the time. Actually, Little Round Top WAS NOT Lee's objective in his attack. Longstreet, once he got into position south of A.P. Hill, was to attack up the Emmittsburg Road in an en eschelon fashion, striking the Federals farther north near Cemetery Hill. Sickles' forward line, as indefensible as it was, nevertheless acted as a breakwater to fragment and blunt the Confederate attack in different sectors of the field, thereby preventing the coordinated jaggernaut envisioned by Lee. Also keep in mind that Sickles only had two divisions. Had he stayed on Cemetery Ridge, his position there was no better defended in that low ground either. Since the Sixth Corps was just arriving and assuming that the Confederates attack wound-up somewhat south from their intended objective, Sickles's two divisions could have been penetrated. With no real estate behind them to buy time for needed reinforcements, the Confederates would have been in Meade's rear immediately. But since there were separate firefights in Devil's Den, Little Round Top, Wheatfield, and Peach Orchard, Lee's men did not have the essential coordination to make the intended attack successful, thereby allowing Meade sufficient time to send in supports. Anyway, regardless of how you feel about the man as a commander, in a sense he is the "hero" of Gettysburg because he was instrumental in having the battlefield memorialized after the war as a result of his tenure on the New York Monuments Commission.
Did he deserve the Medal of Honor? Probably not, but his special pleading before Lincoln secured that honor. From that point his reputation was mired with petty arguments against Meade, including outright falsification of Meade's intention at Gettysburg before the Committee on the Conduct of the War. Quite an interesting man, indeed--a man who, before the war, committed a homicide and was exonerated ; and after the war, working for the U.S. in Spain, tried to carry on an affair with the queen.