It doesn't make sense to say that because Jesus said that He would send the Comforter after He left, and that it would be better for Him to leave so that the Holy Spirit could come. Which means that the Holy Spirit didn't start truly residing inside of people until that point, since after one is saved they then become the temple of God.
When I say "truly residing inside of people" I mean that the Holy Spirit is with us always, we are His temple. An Old testament person had the Holy Spirit taken away from him. Others worried about Him being taken away.
1 Samuel 16:13-14 King James Version (KJV)
13 Then Samuel took the horn of oil, and anointed him in the midst of his brethren: and the Spirit of the Lord came upon David from that day forward. So Samuel rose up, and went to Ramah.
14 But the Spirit of the Lord departed from Saul, and an evil spirit from the Lord troubled him.
The Holy Spirit doesn't depart from us, He resides inside of us. We are His temple. God will never leave us, nor forsake us. Yet, even David had this worry.
Psalm 51:11King James Version (KJV)
11 Cast me not away from thy presence; and take not thy holy spirit from me.
This isn't something we have to worry about, because for us the Holy Spirit is a guarantee.
Ephesians 1:13-14King James Version (KJV)
13 In whom ye also trusted, after that ye heard the word of truth, the gospel of your salvation: in whom also after that ye believed, ye were sealed with that holy Spirit of promise,
14 Which is the earnest of our inheritance until the redemption of the purchased possession, unto the praise of his glory.
The point of all of this being that while the Holy Spirit did interact with Old Testament saints and people from the OT, they didn't experience Him in the same way we do. In this case being that we, and not them, are His temple and He will never leave us, nor forsake us as He did back then to them. He is with us for good.