The Bible teaches that those who have yielded to the Savior’s will (Hebrews 5:8-9) enter directly and immediately into the presence of the Lord after death (Luke 23:43; Philippians 1:23; 2 Corinthians 5:6, 8).
got questions? : What does the Bible say about praying for the dead?
That yielding to the Saviour's Will is essential to be saved, no Catholic doubts.
Hebrews 5 :  And whereas indeed he was the Son of God, he learned obedience by the things which he suffered:  And being consummated, he became, to all that obey him, the cause of eternal salvation.  Called by God a high priest according to the order of Melchisedech.
Yielding to His and His Father's Will according to verse 10 also implies that one acknowledge He is priest, i e sacrificer, "according to the order of Melchisedec" - who sacrificed as "bringing forth bread and wine". So, one must acknowledge that Holy Mass is not just a true memorial of His death, but also therein a true sacrifice.
This was prophecied of old - without this aspect of Catholicism, the prophecy of King David would remain unfulfilled:
Psalm 109 :  The Lord hath sworn, and he will not repent: Thou art a priest for ever according to the order of Melchisedech.
So, yes, we do agree that yielding (i e definitely, not just temporarily and then giving it finally up to sin or unbelief instead) to His Will is indeed necessary to Salvation and doing so adequately (whatever that involves - including acceptance of Holy Mass as a sacrifice for instance) is also sufficient for it. But what about getting to Heaven DIRECTLY after death if this condition is fulfilled?
Gospel According to Saint Luke : Chapter 23  And one of those robbers who were hanged, blasphemed him, saying: If thou be Christ, save thyself and us.  But the other answering, rebuked him, saying: Neither dost thou fear God, seeing thou art condemned under the same condemnation?
 And we indeed justly, for we receive the due reward of our deeds; but this man hath done no evil.  And he said to Jesus: Lord, remember me when thou shalt come into thy kingdom.  And Jesus said to him: Amen I say to thee, this day thou shalt be with me in paradise.
Yes, the robber Dismas was received directly, not into Heaven, but into the Bosom of Abraham which became Paradise when Our Lord's Soul entered it. He came to Heaven along with the others of the Limbo of the Fathers a bit later, but Paradise was given the same day. Here is the Challoner comment:
 In paradise: That is, in the happy state of rest, joy, and peace everlasting. Christ was pleased, by a special privilege, to reward the faith and confession of the penitent thief, with a full discharge of all his sins, both as to the guilt and punishment; and to introduce him immediately after death into the happy society of the saints, whose limbo, that is, the place of their confinement, was now made a paradise by our Lord's going thither.
In other words, true, the robber whom we usually call Dismas was not in Purgatory between earthly life and Paradise, but that doesn't mean Purgatory doesn't exist.
Now, there are two other passages supposedly about every saved person going directly to Heaven when dying:
Epistle Of Saint Paul To The Philippians : Chapter 1 :  But I am straitened between two: having a desire to be dissolved and to be with Christ, a thing by far the better.
Second Epistle Of Saint Paul To The Corinthians : Chapter 5 :  Now he that maketh us for this very thing, is God, who hath given us the pledge of the Spirit.  Therefore having always confidence, knowing that, while we are in the body, we are absent from the Lord.  (For we walk by faith, and not by sight.)  But we are confident, and have a good will to be absent rather from the body, and to be present with the Lord.
I think, for one thing, both these passages of St Paul - at least the verses cited by "got questions?" - would still have been true if St Paul was not sure if he would go through Purgatory or go directly to Heaven.
But in one of the verses not cited, II Cor 5:5, we get a little key to why St Paul seems to have an assurance of getting to Heaven once he dies. Now he that maketh us for this very thing, is God, who hath given us the pledge of the Spirit. God had revealed to him and to the other ones in that "tabernacle" (verse 4, another indication Holy Mass is a sacrifice, since the place where St Paul and his disciples offered it was compared to the tabernacle where sacrifice was offered up between the time of Moses and that of King Solomon) that they would go to Heaven when they died.
Not that every Christian would, but that they would. They had that pledge of the spirit. And they examplify good Christians - it is a dogm of the Council of Trent that no one even a practising Catholic can know without special revelation that he will be saved, but they could very well know that they would not just be saved but also at least in the case of St Paul not go through Purgatory, since they could have such a special revelation.
When we Catholics speak of SAINT Paul or of SAINT Dismas, this means we have special assurance of their persistance and that the Church recognises they went directly to Heaven, without passing through purgatory. Meaning if St Paul had such a revelation it does not on the least contradict his title as given by Catholics of "saint".
As to the claim of the above cited site that even Catholic authorities "admit it is not in the 66 books of the Bible but the Apocrypha" we find support for praying for the dead, first it is not true that we regard the Bible as having only 66 books or the II Book of Maccabees as belonging to Apocrypha. Second it is not the only place, there was also Onesiphorus. As mentioned earlier on this blog.
Hans Georg Lundahl
Bpi, Georges Pompidou
St Thomas of Villanova, Bishop
St Maurice and the Theban Legion, Martyrs